Gravitation

What you'll learn

Master Newton's law of gravitation, variation of g, escape and orbital velocity, and Kepler's laws with clear formulas and a worked example for JEE.

This chapter has

Gravitation — solved practice questions

8 JEE Physics questions with step-by-step solutions. Attempt each, then reveal the answer.

1. Q1easy

   According to Newton's law of gravitation, the force between two point masses is proportional to:

   • AThe separation r
   • BThe inverse square of the separation, 1/r^2
   • CThe inverse of the separation, 1/r
   • DThe square of the separation, r^2
   Show answer & solution

   Correct answer: (B) The inverse square of the separation, 1/r^2

   F = GMm/r^2, so the force is inversely proportional to the square of the separation r.

2. Q2easy

   The gravitational field intensity at any point inside a uniform thin spherical shell is:

   • AZero
   • BMaximum at the centre
   • CEqual to that at the surface
   • DDirected radially inward
   Show answer & solution

   Correct answer: (A) Zero

   By the shell theorem, the net gravitational field everywhere inside a uniform spherical shell is zero, though the potential is non-zero and constant.

3. Q3easy

   Astronauts inside an orbiting satellite feel weightless because:

   • AThere is no gravity in space
   • BThe Earth's gravity is balanced by the Sun's gravity
   • CThey and the satellite are in free fall with the same acceleration
   • DThe satellite is beyond the Earth's gravitational field
   Show answer & solution

   Correct answer: (C) They and the satellite are in free fall with the same acceleration

   The satellite and astronauts are in free fall together; gravity supplies exactly the centripetal acceleration, so the normal (apparent) weight is zero even though g is not zero.

4. Q4medium

   The acceleration due to gravity at a depth equal to half the Earth's radius (assuming uniform density) compared to its surface value g is:

   • Ag/4
   • Bg/2
   • C3g/4
   • Dg
   Show answer & solution

   Correct answer: (B) g/2

   At depth d, g' = g(1 − d/R). For d = R/2, g' = g(1 − 1/2) = g/2.

5. Q5medium

   At what height above the Earth's surface does the acceleration due to gravity reduce to one-fourth of its surface value (R = radius of Earth)?

   • AR/4
   • BR/2
   • C2R
   • DR
   Show answer & solution

   Correct answer: (D) R

   g' = g R^2/(R+h)^2. Setting g' = g/4 gives (R+h)^2 = 4R^2, so R+h = 2R and h = R.

6. Q6medium

   For a planet of mass 2M and radius 2R (where M and R are the Earth's mass and radius), the surface acceleration due to gravity, in terms of the Earth's g, is:

   • Ag/2
   • Bg
   • C2g
   • Dg/4
   Show answer & solution

   Correct answer: (A) g/2

   g' = G(2M)/(2R)^2 = G(2M)/(4R^2) = (1/2)(GM/R^2) = g/2.

7. Q7medium

   The escape velocity from the surface of a planet is v. If another planet has the same radius but four times the mass, its escape velocity is:

   • Av
   • B√2 v
   • C2v
   • D4v
   Show answer & solution

   Correct answer: (C) 2v

   Escape velocity v_e = √(2GM/R) is proportional to √M for fixed R. Four times the mass multiplies v_e by √4 = 2, giving 2v.

8. Q8medium

   For a satellite in a circular orbit of radius r, if its kinetic energy is K, then its total mechanical energy and potential energy are respectively:

   • A+K and −K
   • B−K and −2K
   • C−2K and −K
   • D+2K and +K
   Show answer & solution

   Correct answer: (B) −K and −2K

   For a circular orbit, KE = GMm/2r = K, PE = −GMm/r = −2K, and total energy E = KE + PE = −K.

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