Acceleration Due to Gravity

Searching for a Physics Tutor? If Acceleration due to Gravity, variation of g, effective g or NEET/JEE numericals are not clear, contact Kumar Sir.

Phone: +91-9958461445 | Email: kumarsirphysics@gmail.com | Website: kumarphysicsclasses.com

WhatsApp Kumar SirVisit WebsiteEmail Kumar Sir
g

Acceleration Due to Gravity

Master acceleration due to gravity, relation between g and G, variation with height, depth, latitude, rotation, effective g, numericals and PYQs.

CBSENEETJEE MainJEE AdvancedIBIGCSEA-Level

Acceleration Due to Gravity

Acceleration due to gravity is the acceleration produced in a freely falling body because of Earth's gravitational pull. Near Earth's surface its standard value is approximately 9.8 m s-2, directed toward the centre of Earth.

g = 9.8 m s-2

Falling Object Near Earth

g downward

Weight Direction

W = mg

Gravity Field Lines

towards centre

Relation Between g and G

For a mass m on Earth's surface, Newton's law gives gravitational force as F = GMm/R2. The same force is called weight, F = mg. Equating both expressions gives the relation between g and G.

F = GMm/R2, F = mg, therefore g = GM/R2
G: universal gravitational constant.
M: mass of Earth.
R: radius of Earth.
g: acceleration due to gravity at Earth's surface.
Earth mass MRadius Rmg = GMm/R2

Variation of g With Height

At height h above Earth, the distance from Earth's centre becomes R+h, so g decreases with height.

gh = GM/(R+h)2
gh = g(R/(R+h))2
For h << R, gh approx g(1 - 2h/R)

Height Graph

hg

g decreases non-linearly with height.

Example

At height h = R, find gh.

Show Answer
gh = g(R/(2R))2 = g/4. Exam tip: use distance from centre.

Small Height

For h = R/100, approximate gh.

Show Answer
gh approx g(1 - 2/100) = 0.98g. Common mistake: using 1 - h/R.

Variation of g With Depth

Inside Earth, assuming uniform density, only the mass enclosed within the radius contributes. Therefore g decreases linearly with depth and becomes zero at Earth's centre.

gd = g(1 - d/R)

Depth Diagram

depth dcentre

g vs Depth

dglinear decrease

Variation of g With Latitude and Rotation

Earth rotates, so effective gravity is reduced by centrifugal effect. The reduction is maximum at the equator and zero at the poles.

g' = g - Romega2cos2lambda
At equator: geq = g - Romega2
At poles: gpole = g

Rotating Earth

equatorpole

Latitude Angle

lambda

Exam Point

g is minimum at equator and maximum at poles because centrifugal effect is largest at equator. Earth's shape also contributes slightly.

Effective g

Effective gravity is the gravity felt in an accelerating frame. It explains apparent weight changes in lifts and weightlessness in free fall.

Lift Moving Upward

N = m(g + a)

a upward

Lift Moving Downward

N = m(g - a)

a downward

Freely Falling Lift

N = 0

When a = g downward, apparent weight becomes zero. Gravity is not absent; the person and lift fall together.

Searching for a Physics Tutor? If Acceleration due to Gravity, variation of g, effective g or NEET/JEE numericals are not clear, contact Kumar Sir.

Phone: +91-9958461445 | Email: kumarsirphysics@gmail.com | Website: kumarphysicsclasses.com

WhatsApp Kumar SirVisit WebsiteEmail Kumar Sir

Important Formula Table

ConceptFormulaMeaningExam Tip
Surface gg = GM/R2Gravity at Earth's surface.Use Earth radius R.
Heightgh = GM/(R+h)2Gravity at height h.Use R+h, not h.
Height ratiogh = g(R/(R+h))2Compare with surface g.Best for ratio problems.
Small heightgh approx g(1 - 2h/R)Approximation for h much smaller than R.Only for small h.
Depthgd = g(1 - d/R)Uniform-density Earth model.Linear with depth.
Equatorgeq = g - Romega2Minimum effective g.Maximum rotation effect.
Polegpole = gNo centrifugal reduction.Maximum g.
Upward liftN = m(g+a)Apparent weight increases.Feels heavier.
Downward liftN = m(g-a)Apparent weight decreases.Feels lighter.
Free fallN = 0Weightlessness.Gravity still acts.

Important Graphs

g vs Height

hg

Decreasing curve.

g vs Depth

dg

Straight line to zero at centre.

g vs Distance From Centre

rgR

Inside Earth g increases linearly; outside it decreases as 1/r2.

g vs Latitude

latitudeg

Minimum at equator, maximum at poles.

Apparent Weight vs Lift Acceleration

aN

For upward acceleration, apparent weight increases linearly.

Applications

1. Falling Body Near Earth

Concept: Freely falling objects accelerate downward.

Formula: g = 9.8 m s-2.

Exam Tip: Ignore air resistance unless stated.

2. Satellite Height

Concept: g decreases at altitude.

Formula: gh = GM/(R+h)2.

Exam Tip: Distance is R+h.

3. Mine / Depth Gravity

Concept: g decreases inside Earth.

Formula: gd = g(1-d/R).

Exam Tip: Use depth formula, not height formula.

4. Equator and Poles

Concept: Rotation reduces g most at equator.

Formula: geq = g - Romega2.

Exam Tip: Pole value is larger.

5. Lift Apparent Weight

Concept: Normal reaction changes in accelerating lift.

Formula: N = m(g+a) or m(g-a).

Exam Tip: Direction of acceleration decides sign.

6. Astronaut Weightlessness

Concept: Astronaut and spacecraft fall together.

Formula: N = 0.

Exam Tip: g is not zero in orbit.

7. Free Fall

Concept: Only gravity acts.

Formula: a = g downward.

Exam Tip: Apparent weight is zero in free fall.

8. Rotating Earth

Concept: Centrifugal effect reduces effective g.

Formula: reduction = Romega2cos2lambda.

Exam Tip: Reduction is zero at poles.

9. Mountain Height Effect

Concept: g decreases on mountains.

Formula: gh approx g(1-2h/R).

Exam Tip: Small-height approximation is useful.

10. Gravity Inside Earth

Concept: g becomes zero at centre.

Formula: g proportional to r inside uniform Earth.

Exam Tip: Inside and outside graphs are different.

High-Quality Solved Numericals

CBSE Numerical

Question: Find g at height R above Earth.

Show Answer

Given: h=R. Formula: gh=g(R/(R+h))2. Calculation: g(R/2R)2=g/4. Final Answer: 2.45 m s-2. Exam Tip: Use R+h. Common Mistake: Using h alone.

NEET Numerical

Question: Find g at depth R/2.

Show Answer

Given: d=R/2. Formula: gd=g(1-d/R). Calculation: g(1-1/2)=g/2. Final Answer: 4.9 m s-2. Tip: Depth is linear. Mistake: Squaring depth term.

JEE Main Numerical

Question: A 60 kg person is in a lift accelerating upward at 2 m s-2. Find apparent weight.

Show Answer

Given: m=60 kg, a=2. Formula: N=m(g+a). Calculation: N=60(9.8+2)=708 N. Final Answer: 708 N. Tip: Upward acceleration increases apparent weight. Mistake: Using g-a.

JEE Advanced Numerical

Question: At what height is g reduced to g/9?

Show Answer

Formula: gh/g=(R/(R+h))2. Calculation: 1/9=(R/(R+h))2, so R+h=3R. Final Answer: h=2R. Tip: Take square root. Mistake: Writing h=3R.

IB Numerical

Question: A lift accelerates downward at 3 m s-2. Find apparent weight of 50 kg person.

Show Answer

Formula: N=m(g-a). Calculation: N=50(9.8-3)=340 N. Final Answer: 340 N. Tip: Downward acceleration reduces normal reaction. Mistake: Calling it actual weight.

IGCSE Numerical

Question: Weight of 20 kg body near Earth?

Show Answer

Formula: W=mg. Calculation: W=20 x 9.8 = 196 N. Final Answer: 196 N. Tip: Unit of weight is newton. Mistake: Writing kg.

A-Level Numerical

Question: If g decreases by 2% at small height h, find h/R.

Show Answer

Formula: gh approx g(1-2h/R). Calculation: 2h/R=0.02. Final Answer: h/R=0.01. Tip: Percent reduction equals 2h/R. Mistake: h/R=0.02.

NEET Question Bank

Authentic years are mentioned only when known; otherwise these are NEET exam-style questions.

NEET Exam-style Question 1

What is the standard value of g near Earth?

Show Answer
9.8 m s-2.

NEET Exam-style Question 2

Direction of g is?

Show Answer
Towards Earth's centre.

NEET Exam-style Question 3

Relation between g and G?

Show Answer
g = GM/R2.

NEET Exam-style Question 4

g at height h is?

Show Answer
GM/(R+h)2.

NEET Exam-style Question 5

g at height R is?

Show Answer
g/4.

NEET Exam-style Question 6

Small-height formula?

Show Answer
gh approx g(1-2h/R).

NEET Exam-style Question 7

g at depth d is?

Show Answer
g(1-d/R).

NEET Exam-style Question 8

g at Earth's centre is?

Show Answer
Zero.

NEET Exam-style Question 9

Where is g minimum due to rotation?

Show Answer
At equator.

NEET Exam-style Question 10

Where is g maximum?

Show Answer
At poles.

NEET Exam-style Question 11

Apparent weight in upward lift?

Show Answer
N=m(g+a).

NEET Exam-style Question 12

Apparent weight in downward lift?

Show Answer
N=m(g-a).

NEET Exam-style Question 13

Apparent weight in free fall?

Show Answer
Zero.

NEET Exam-style Question 14

Is g zero in orbit?

Show Answer
No, it is reduced but not zero.

NEET Exam-style Question 15

Weightlessness means?

Show Answer
Normal reaction is zero.

NEET Exam-style Question 16

g vs depth graph is?

Show Answer
Straight decreasing line.

NEET Exam-style Question 17

g vs height graph is?

Show Answer
Decreasing inverse-square curve.

NEET Exam-style Question 18

g at depth R/2 is?

Show Answer
g/2.

NEET Exam-style Question 19

g at height 2R is?

Show Answer
g/9.

NEET Exam-style Question 20

At equator formula?

Show Answer
geq=g-Romega2.

NEET Exam-style Question 21

At pole formula?

Show Answer
gpole=g.

NEET Exam-style Question 22

Latitude formula includes which factor?

Show Answer
cos2lambda.

NEET Exam-style Question 23

If lift accelerates downward with a=g, N is?

Show Answer
Zero.

NEET Exam-style Question 24

If lift accelerates upward with a=g, N is?

Show Answer
2mg.

NEET Exam-style Question 25

For small h, percentage decrease in g is?

Show Answer
Approximately 2h/R x 100 percent.

NEET Exam-style Question 26

For depth R/4, g is?

Show Answer
3g/4.

NEET Exam-style Question 27

For height R/2, g is?

Show Answer
4g/9.

NEET Exam-style Question 28

g depends on Earth mass how?

Show Answer
Directly proportional to M.

NEET Exam-style Question 29

g depends on Earth radius how?

Show Answer
Inversely proportional to R2.

NEET Exam-style Question 30

Unit of g?

Show Answer
m s-2 or N kg-1.

NEET Exam-style Question 31

Dimension of g?

Show Answer
[LT-2].

NEET Exam-style Question 32

Why g changes with height?

Show Answer
Distance from Earth's centre increases.

NEET Exam-style Question 33

Why g changes with depth?

Show Answer
Effective enclosed mass decreases.

NEET Exam-style Question 34

Effective g in accelerating frame is?

Show Answer
Apparent gravitational acceleration felt in the frame.

NEET Exam-style Question 35

If g=10 and a=2 upward, N/m is?

Show Answer
12 N kg-1.

NEET Exam-style Question 36

If g=10 and a=2 downward, N/m is?

Show Answer
8 N kg-1.

NEET Exam-style Question 37

On a mountain, g is?

Show Answer
Less than at sea level.

NEET Exam-style Question 38

In a mine, g is?

Show Answer
Less than at surface.

NEET Exam-style Question 39

Falling lift apparent weight?

Show Answer
Zero.

NEET Exam-style Question 40

At what height is g=g/4?

Show Answer
h=R.

NEET Exam-style Question 41

At what depth is g=g/4?

Show Answer
d=3R/4.

NEET Exam-style Question 42

At what depth is g zero?

Show Answer
d=R, at centre.

NEET Exam-style Question 43

At latitude 90 degree, reduction due to rotation?

Show Answer
Zero.

NEET Exam-style Question 44

At latitude 0 degree, reduction due to rotation?

Show Answer
Romega2.

NEET Exam-style Question 45

Actual weight is?

Show Answer
mg.

NEET Exam-style Question 46

Apparent weight is?

Show Answer
Normal reaction N.

NEET Exam-style Question 47

Why astronauts float?

Show Answer
They are in continuous free fall with spacecraft.

NEET Exam-style Question 48

Which formula is used inside Earth?

Show Answer
gd=g(1-d/R).

NEET Exam-style Question 49

Which formula is used above Earth?

Show Answer
gh=g(R/(R+h))2.

NEET Exam-style Question 50

Weightlessness means gravity absent: true or false?

Show Answer
False.

JEE Main Question Bank

JEE Main 1

Find g at h=R.

Show Answer
g/4.

JEE Main 2

Find g at h=2R.

Show Answer
g/9.

JEE Main 3

Find g at d=R/3.

Show Answer
2g/3.

JEE Main 4

Find d if gd=g/5.

Show Answer
d=4R/5.

JEE Main 5

Find h if gh=g/16.

Show Answer
R/(R+h)=1/4, so h=3R.

JEE Main 6

For small h=R/200, g decrease percent?

Show Answer
1 percent.

JEE Main 7

Person in lift upward a=3, m=70, g=10. N?

Show Answer
N=70(13)=910 N.

JEE Main 8

Lift downward a=4, m=50, g=10. N?

Show Answer
N=300 N.

JEE Main 9

Free-fall lift reading of weighing scale?

Show Answer
Zero.

JEE Main 10

At pole centrifugal correction?

Show Answer
Zero.

JEE Main 11

At equator correction?

Show Answer
Romega2.

JEE Main 12

At latitude 60 degree correction factor?

Show Answer
Romega2cos260 = Romega2/4.

JEE Main 13

g vs depth slope?

Show Answer
-g/R.

JEE Main 14

Inside Earth, g is proportional to?

Show Answer
Distance from centre r.

JEE Main 15

Outside Earth, g is proportional to?

Show Answer
1/r2.

JEE Main 16

At centre of uniform Earth, g?

Show Answer
Zero.

JEE Main 17

At surface g is maximum in uniform Earth graph?

Show Answer
Yes, for ideal uniform sphere.

JEE Main 18

If Earth mass doubles and radius same, g?

Show Answer
2g.

JEE Main 19

If Earth radius doubles and mass same, g?

Show Answer
g/4.

JEE Main 20

If Earth density same and radius doubles, surface g?

Show Answer
2g because M proportional R3.

JEE Main 21

If g=9.8, downward lift a=9.8, N?

Show Answer
Zero.

JEE Main 22

If apparent weight is half, downward acceleration?

Show Answer
a=g/2.

JEE Main 23

If apparent weight doubles, upward acceleration?

Show Answer
a=g.

JEE Main 24

Mountain height small h reduces g by?

Show Answer
2gh/R in absolute value.

JEE Main 25

Depth d reduces g by?

Show Answer
gd/R.

JEE Main 26

Height formula has square because?

Show Answer
Gravitational field follows inverse-square law.

JEE Main 27

Depth formula is linear because?

Show Answer
Enclosed mass decreases as r3 inside uniform sphere.

JEE Main 28

At h=R/10 exact g ratio?

Show Answer
1/(1.1)2 = 100/121.

JEE Main 29

At h=R/10 approximate g ratio?

Show Answer
1 - 0.2 = 0.8.

JEE Main 30

At d=R/10 g ratio?

Show Answer
0.9.

JEE Main 31

Effective g in upward lift?

Show Answer
g+a.

JEE Main 32

Effective g in downward lift?

Show Answer
g-a.

JEE Main 33

Effective g in freely falling frame?

Show Answer
Zero.

JEE Main 34

Why g lower at equator?

Show Answer
Centrifugal effect and larger equatorial radius.

JEE Main 35

g vs latitude trend?

Show Answer
Increases from equator to pole.

JEE Main 36

For lambda=45 degree, rotational reduction?

Show Answer
Romega2/2.

JEE Main 37

At what depth g=3g/4?

Show Answer
d=R/4.

JEE Main 38

At what height g=4g/9?

Show Answer
h=R/2.

JEE Main 39

If g graph vs r inside is line through origin, slope?

Show Answer
g/R.

JEE Main 40

Outside graph g vs r at r=2R?

Show Answer
g/4.

JEE Main 41

At r=R/2 inside Earth, g?

Show Answer
g/2.

JEE Main 42

At r=0 inside Earth, g?

Show Answer
0.

JEE Main 43

At r=3R outside Earth, g?

Show Answer
g/9.

JEE Main 44

Scale reads 800 N normally. Upward a=0.25g reading?

Show Answer
1000 N.

JEE Main 45

Scale reads 800 N normally. Downward a=0.25g reading?

Show Answer
600 N.

JEE Main 46

Orbital weightlessness due to?

Show Answer
Continuous free fall.

JEE Main 47

g in orbit at low altitude is approximately?

Show Answer
Close to surface g, not zero.

JEE Main 48

Why use approximation only for h<<R?

Show Answer
Binomial expansion neglects higher powers of h/R.

JEE Main 49

Dimensional formula of g?

Show Answer
[LT-2].

JEE Main 50

Unit N kg-1 equals?

Show Answer
m s-2.

JEE Advanced Question Bank

These questions focus on g variation graphs, non-uniform density ideas, rotating frame, lift and multi-step gravitation.

JEE Advanced 1

For uniform Earth, derive g at radius r inside.

Show Answer
Enclosed mass M(r)=M r3/R3. Field = GM(r)/r2 = GMr/R3 = g r/R.

JEE Advanced 2

At depth d, show gd=g(1-d/R).

Show Answer
Inside radius r=R-d. Since g(r)=g r/R, gd=g(R-d)/R=g(1-d/R).

JEE Advanced 3

At what r inside Earth is g half surface value?

Show Answer
g r/R = g/2, so r=R/2. Depth d=R/2.

JEE Advanced 4

At what r outside Earth is g half surface value?

Show Answer
gR2/r2=g/2, so r=sqrt2 R. Height=(sqrt2-1)R.

JEE Advanced 5

Compare depth and height for same small reduction x.

Show Answer
Depth reduction x=d/R; height reduction x=2h/R. For same x, d=2h.

JEE Advanced 6

For density rho constant, express surface g.

Show Answer
M=(4/3)pi R3rho, so g=GM/R2=(4/3)pi G rho R.

JEE Advanced 7

If same density planet has radius 3R, surface g?

Show Answer
g proportional to R, so 3g.

JEE Advanced 8

If mass same and radius halved, surface g?

Show Answer
4g.

JEE Advanced 9

If radius same and mass halved, surface g?

Show Answer
g/2.

JEE Advanced 10

Find effective g at latitude lambda.

Show Answer
g' = g - Romega2cos2lambda in simplified model.

JEE Advanced 11

At latitude 60 degree, reduction relative to equator?

Show Answer
Reduction is one-fourth of equatorial centrifugal reduction.

JEE Advanced 12

If Earth stops rotating, g at equator changes how?

Show Answer
It increases by approximately Romega2.

JEE Advanced 13

Lift accelerates upward with a variable a. Slope of N vs a?

Show Answer
N=m(g+a), slope=m.

JEE Advanced 14

Lift accelerates downward. Slope of N vs a?

Show Answer
N=m(g-a), slope=-m.

JEE Advanced 15

Scale reads 0.75mg in lift. Find downward acceleration.

Show Answer
m(g-a)=0.75mg, so a=0.25g.

JEE Advanced 16

Scale reads 1.25mg in lift. Find acceleration.

Show Answer
m(g+a)=1.25mg, so a=0.25g upward.

JEE Advanced 17

Can N be negative in downward lift formula?

Show Answer
Physical contact is lost before negative N; for a>g, N becomes zero and person floats relative to lift.

JEE Advanced 18

Why g is not zero in spacecraft?

Show Answer
Gravity provides centripetal acceleration; normal reaction is zero because spacecraft and astronaut free fall together.

JEE Advanced 19

At r=R/3 inside uniform Earth, g?

Show Answer
g/3.

JEE Advanced 20

At r=3R outside Earth, g?

Show Answer
g/9.

JEE Advanced 21

Graph of g vs r has maximum where?

Show Answer
At r=R for uniform Earth.

JEE Advanced 22

Inside non-uniform Earth, is g necessarily linear?

Show Answer
No. Linear result needs uniform density.

JEE Advanced 23

If density increases toward centre, qualitative g-depth graph?

Show Answer
It is not simply linear; enclosed mass changes differently with radius.

JEE Advanced 24

Derive small-height approximation.

Show Answer
gh/g=(1+h/R)-2 approx 1-2h/R by binomial expansion.

JEE Advanced 25

Next correction term in height expansion?

Show Answer
(1+x)-2 = 1-2x+3x2-..., so term is +3h2/R2.

JEE Advanced 26

At h=R/100, exact vs approximate ratio?

Show Answer
Exact=1/(1.01)2; approximate=0.98, close to exact 0.9803.

JEE Advanced 27

At h=R/2, why approximation is poor?

Show Answer
h/R is not small; exact ratio is 4/9 but approximation gives 0.

JEE Advanced 28

Find h for 1% decrease in g using approximation.

Show Answer
2h/R=0.01, so h=R/200.

JEE Advanced 29

Find depth for 1% decrease in g.

Show Answer
d/R=0.01, so d=R/100.

JEE Advanced 30

Compare the above height and depth.

Show Answer
Depth is twice the height for same small percentage decrease.

JEE Advanced 31

What is apparent weight at top of projectile motion?

Show Answer
If only gravity acts, apparent weight in projectile's free-fall frame is zero.

JEE Advanced 32

What is effective g in a frame accelerating horizontally with a?

Show Answer
Magnitude sqrt(g2+a2), direction tilted opposite frame acceleration.

JEE Advanced 33

A pendulum in horizontally accelerating lift aligns with?

Show Answer
Effective gravity vector, resultant of g downward and pseudo acceleration opposite horizontal acceleration.

JEE Advanced 34

Weight at equator if omega increases?

Show Answer
Effective weight decreases.

JEE Advanced 35

Critical omega for zero apparent weight at equator?

Show Answer
Set g-Romega2=0, so omega=sqrt(g/R).

JEE Advanced 36

Why pole unaffected by rotation in simplified formula?

Show Answer
Distance from rotation axis is zero at pole, so centrifugal effect is zero.

JEE Advanced 37

At latitude lambda, distance from axis?

Show Answer
R cos lambda.

JEE Advanced 38

Centrifugal acceleration radial from axis magnitude?

Show Answer
omega2R cos lambda; vertical radial component gives omega2R cos2lambda.

JEE Advanced 39

If Earth radius becomes R/2 at same mass, escape aside, g?

Show Answer
4g.

JEE Advanced 40

If Earth mass and radius both double, g?

Show Answer
g/2, because M factor 2 and R2 factor 4.

JEE Advanced 41

If density and radius both double effect on g?

Show Answer
g proportional rho R, so 4g.

JEE Advanced 42

What is field unit equivalence?

Show Answer
N kg-1 = m s-2.

JEE Advanced 43

Why g has same unit as acceleration?

Show Answer
It is force per unit mass and also acceleration of free fall.

JEE Advanced 44

In a downward accelerating lift with a>g, what happens?

Show Answer
The person loses contact; N=0 physically.

JEE Advanced 45

Find g at h such that R+h=5R.

Show Answer
g/25.

JEE Advanced 46

Find h if gh=4g/25.

Show Answer
R/(R+h)=2/5, so R+h=5R/2 and h=3R/2.

JEE Advanced 47

Find d if gd=4g/25.

Show Answer
1-d/R=4/25, so d=21R/25.

JEE Advanced 48

Same g value can occur where?

Show Answer
One point inside Earth and one point outside Earth can have same g less than surface g.

JEE Advanced 49

For g'=g/2 outside, r?

Show Answer
r=sqrt2 R.

JEE Advanced 50

For g'=g/2 inside, r?

Show Answer
r=R/2.

IB / IGCSE / A-Level Questions

25 IB Questions

  1. Define g.
    Show Answer
    Gravitational field strength or free-fall acceleration.
  2. Unit of g?
    Show Answer
    N kg-1 or m s-2.
  3. State g-G relation.
    Show Answer
    g=GM/R2.
  4. Why g changes with altitude?
    Show Answer
    Distance from Earth centre changes.
  5. Formula at height?
    Show Answer
    g(R/(R+h))2.
  6. Formula at depth?
    Show Answer
    g(1-d/R).
  7. g at centre?
    Show Answer
    Zero.
  8. g at poles vs equator?
    Show Answer
    Greater at poles.
  9. What is apparent weight?
    Show Answer
    Normal reaction.
  10. Weightlessness means?
    Show Answer
    N=0.
  11. Lift upward formula?
    Show Answer
    N=m(g+a).
  12. Lift downward formula?
    Show Answer
    N=m(g-a).
  13. Free fall formula?
    Show Answer
    N=0.
  14. Graph g-depth?
    Show Answer
    Linear decrease.
  15. Graph g-height?
    Show Answer
    Curved decrease.
  16. Dimension of g?
    Show Answer
    [LT-2].
  17. What causes latitude effect?
    Show Answer
    Rotation and Earth shape.
  18. Small height approximation?
    Show Answer
    g(1-2h/R).
  19. When valid?
    Show Answer
    h much smaller than R.
  20. Why astronauts float?
    Show Answer
    Free fall with spacecraft.
  21. Is gravity zero in orbit?
    Show Answer
    No.
  22. Define effective g.
    Show Answer
    Gravity felt in accelerating frame.
  23. What is g at h=R?
    Show Answer
    g/4.
  24. What is g at d=R/2?
    Show Answer
    g/2.
  25. One exam trap?
    Show Answer
    Confusing G and g.

25 IGCSE Questions

  1. What is gravity?
    Show Answer
    Attraction due to mass.
  2. What is g on Earth?
    Show Answer
    About 9.8 m s-2.
  3. Direction of weight?
    Show Answer
    Downward, toward Earth centre.
  4. Weight formula?
    Show Answer
    W=mg.
  5. Unit of weight?
    Show Answer
    Newton.
  6. Does mass change on Moon?
    Show Answer
    No.
  7. Does weight change on Moon?
    Show Answer
    Yes.
  8. What is free fall?
    Show Answer
    Motion under gravity only.
  9. What is apparent weight?
    Show Answer
    Scale reading.
  10. Lift going up feels?
    Show Answer
    Heavier if accelerating upward.
  11. Lift going down feels?
    Show Answer
    Lighter if accelerating downward.
  12. Free fall scale reads?
    Show Answer
    Zero.
  13. On mountain g is?
    Show Answer
    Slightly less.
  14. In mine g is?
    Show Answer
    Slightly less.
  15. At centre of Earth g is?
    Show Answer
    Zero.
  16. What is field strength?
    Show Answer
    Force per unit mass.
  17. Unit of field strength?
    Show Answer
    N kg-1.
  18. What causes falling?
    Show Answer
    Gravitational force.
  19. Does air resistance affect ideal g?
    Show Answer
    No, ideal free fall ignores it.
  20. At poles g is?
    Show Answer
    Slightly greater.
  21. At equator g is?
    Show Answer
    Slightly smaller.
  22. Why astronauts appear weightless?
    Show Answer
    No support force.
  23. Is weight a force?
    Show Answer
    Yes.
  24. Is g a force?
    Show Answer
    No, it is acceleration/field strength.
  25. Common unit mistake?
    Show Answer
    Writing weight in kg.

25 A-Level Questions

  1. Derive g=GM/R2.
    Show Answer
    Equate GMm/R2 and mg.
  2. Derive height formula.
    Show Answer
    Replace R by R+h in field formula.
  3. Derive depth formula.
    Show Answer
    Use enclosed mass for uniform density Earth.
  4. Explain non-uniform density issue.
    Show Answer
    Depth relation is not exactly linear.
  5. Rotation correction?
    Show Answer
    Romega2cos2lambda.
  6. Critical omega?
    Show Answer
    sqrt(g/R).
  7. Effective g in horizontal acceleration?
    Show Answer
    sqrt(g2+a2).
  8. Pendulum tilt in accelerating frame?
    Show Answer
    tan theta = a/g.
  9. Lift upward apparent weight?
    Show Answer
    m(g+a).
  10. Lift downward apparent weight?
    Show Answer
    m(g-a).
  11. Contact loss condition?
    Show Answer
    Downward acceleration at least g.
  12. Graph inside Earth?
    Show Answer
    Linear through origin versus r.
  13. Graph outside Earth?
    Show Answer
    Inverse-square decrease.
  14. Maximum g in ideal graph?
    Show Answer
    At surface.
  15. Small-height expansion?
    Show Answer
    1-2h/R+3h2/R2...
  16. Exact ratio at h=R/2?
    Show Answer
    4/9.
  17. Approx ratio at h=R/100?
    Show Answer
    0.98.
  18. Depth for 20% decrease?
    Show Answer
    d=0.2R.
  19. Height for 20% small decrease?
    Show Answer
    h=0.1R approximately.
  20. Why approximation may fail?
    Show Answer
    h/R not small.
  21. g if M doubles R doubles?
    Show Answer
    g/2.
  22. g if density same R doubles?
    Show Answer
    2g.
  23. Meaning of N=0?
    Show Answer
    No support force.
  24. Why orbiting astronauts weightless?
    Show Answer
    They share centripetal free fall.
  25. Common A-Level trap?
    Show Answer
    Assuming g is zero in orbit.

Assertion Reason Questions

AR 1

Assertion: g decreases with height. Reason: Distance from Earth's centre increases.

Show Answer
Both true and reason explains assertion.

AR 2

Assertion: g decreases linearly with depth. Reason: Uniform Earth model gives enclosed mass effect.

Show Answer
Both true and reason explains assertion.

AR 3

Assertion: g is zero in orbit. Reason: Astronauts are weightless.

Show Answer
Assertion false; reason true in apparent sense.

AR 4

Assertion: Apparent weight is zero in free fall. Reason: Normal reaction is zero.

Show Answer
Both true and reason explains assertion.

AR 5

Assertion: Upward lift increases apparent weight. Reason: N=m(g+a).

Show Answer
Both true and reason explains assertion.

AR 6

Assertion: Downward lift decreases apparent weight. Reason: N=m(g-a).

Show Answer
Both true and reason explains assertion.

AR 7

Assertion: g is minimum at equator. Reason: Centrifugal effect is maximum at equator.

Show Answer
Both true and reason explains assertion.

AR 8

Assertion: g is maximum at poles. Reason: Centrifugal effect is zero there.

Show Answer
Both true; reason explains major rotation contribution.

AR 9

Assertion: G and g are same. Reason: Both are used in gravitation.

Show Answer
Assertion false; reason true but not explanation.

AR 10

Assertion: Small-height formula works for h=R. Reason: h is height.

Show Answer
Both false for approximation validity.

AR 11

Assertion: At centre of Earth g is zero. Reason: Symmetric pulls cancel.

Show Answer
Both true and reason explains assertion.

AR 12

Assertion: At height R, g becomes g/2. Reason: Distance doubles.

Show Answer
Assertion false; it becomes g/4. Reason true.

AR 13

Assertion: At depth R/2, g becomes g/2. Reason: g decreases linearly with depth.

Show Answer
Both true and reason explains assertion.

AR 14

Assertion: Weight is measured in newton. Reason: Weight is force.

Show Answer
Both true and reason explains assertion.

AR 15

Assertion: g unit can be N kg-1. Reason: g is force per unit mass.

Show Answer
Both true and reason explains assertion.

AR 16

Assertion: In orbit, normal reaction is zero. Reason: Spacecraft and astronaut free fall together.

Show Answer
Both true and reason explains assertion.

AR 17

Assertion: g at mountains is less. Reason: R+h is greater than R.

Show Answer
Both true and reason explains assertion.

AR 18

Assertion: g in mines is less. Reason: Only enclosed mass contributes effectively.

Show Answer
Both true and reason explains assertion.

AR 19

Assertion: g vs height is linear. Reason: g follows inverse square law.

Show Answer
Assertion false; reason true.

AR 20

Assertion: g vs depth is linear in uniform Earth. Reason: gd=g(1-d/R).

Show Answer
Both true and reason explains assertion.

AR 21

Assertion: Effective g can be larger than g. Reason: Lift accelerating upward gives g+a.

Show Answer
Both true and reason explains assertion.

AR 22

Assertion: Effective g can be zero. Reason: Freely falling frame has a=g downward.

Show Answer
Both true and reason explains assertion.

AR 23

Assertion: At poles cos lambda is zero. Reason: lambda=90 degrees.

Show Answer
Both true and reason explains zero rotational reduction.

AR 24

Assertion: At equator cos lambda is one. Reason: lambda=0 degrees.

Show Answer
Both true and reason explains maximum reduction.

AR 25

Assertion: Apparent weight equals actual weight always. Reason: N is always mg.

Show Answer
Both false in accelerating frames.

AR 26

Assertion: g depends on planet mass. Reason: g=GM/R2.

Show Answer
Both true and reason explains assertion.

AR 27

Assertion: g depends on planet radius. Reason: Radius appears squared in denominator.

Show Answer
Both true and reason explains assertion.

AR 28

Assertion: In free fall, actual gravity vanishes. Reason: Scale reads zero.

Show Answer
Assertion false; reason true for apparent weight.

AR 29

Assertion: Inside Earth, outside formula GM/r2 with total M fails. Reason: Not all mass contributes as enclosed mass.

Show Answer
Both true and reason explains assertion.

AR 30

Assertion: Latitude affects g. Reason: Earth rotates.

Show Answer
Both true and reason explains major effect.

Case Study Questions

Lift and Apparent Weight

Passage: A person of mass m stands on a scale in a lift. The scale reads normal reaction N.

  1. What is N for upward acceleration?
  2. What is N for downward acceleration?
  3. When is N zero?
Show Answer

Answers: m(g+a), m(g-a), free fall. Explanation: Apparent weight is normal reaction, not always mg.

Astronaut Weightlessness

Passage: Astronauts orbit Earth and float inside spacecraft.

  1. Is gravity zero?
  2. Why do they float?
  3. What is N?
Show Answer

Answers: No; spacecraft and astronaut free fall together; N=0. Explanation: Weightlessness means absence of support force.

Gravity on Mountain

Passage: A student carries a spring balance from sea level to a mountain.

  1. Does g increase or decrease?
  2. Which formula applies?
  3. What approximation is used for small height?
Show Answer

Answers: Decrease; g(R/(R+h))2; g(1-2h/R). Explanation: Distance from Earth's centre increases.

Gravity Inside Earth

Passage: A mine goes to depth d below Earth's surface.

  1. Formula for g at depth?
  2. What happens at centre?
  3. Graph shape?
Show Answer

Answers: g(1-d/R); zero; straight line decrease. Explanation: In uniform Earth model, enclosed mass controls gravity.

Earth Rotation and Latitude

Passage: Earth rotates with angular speed omega. Effective g varies from equator to poles.

  1. Where is g minimum?
  2. Where is g maximum?
  3. What is latitude formula?
Show Answer

Answers: Equator; poles; g'=g-Romega2cos2lambda. Explanation: Centrifugal effect is largest at equator and zero at poles.

Common Student Mistakes

Confusing G and g

G is universal constant; g is local acceleration or field strength.

Using Height Formula for Depth

Height uses inverse square with R+h; depth uses linear formula g(1-d/R).

Forgetting Small-Height Limit

g(1-2h/R) is valid only when h is much smaller than R.

Wrong Lift Sign

Upward acceleration uses g+a; downward acceleration uses g-a.

Saying g Is Zero in Orbit

g is not zero in orbit; normal reaction is zero.

Ignoring Latitude Effect

Effective g is slightly smaller at equator due to rotation.

Searching for a Physics Tutor? If Acceleration due to Gravity, variation of g, effective g or NEET/JEE numericals are not clear, contact Kumar Sir.

Phone: +91-9958461445 | Email: kumarsirphysics@gmail.com | Website: kumarphysicsclasses.com

WhatsApp Kumar SirVisit WebsiteEmail Kumar Sir
Scroll to Top