 # Gravitation Multiple Choice Questions

In this page we have Gravitation Multiple Choice Questions for JEE Main/Advanced . Hope you like them and do not forget to like , social share and comment at the end of the page.

## Multiple Choice Questions

Question 1
Which of the following is true for Uniform Solid sphere of Mass M and radius b
(a) for r > b,Gravitational field decreases as r is increased
(b) for r< b, Gravitational field increased as r is increased
(c) Gravitational Field at r=0 is equal to 0
(d) Gravitational field at the r=b is $\frac {GM}{b^2}$

Question 2
Let P denotes the Gravitational potential and F denotes the Gravitational Field
What all relation are true for a uniform spherical shell
(a) P≠0 inside the shell and it is constant inside the shell
(b) E≠0 inside the shell and it is constant inside the shell
(c) E=0 at all the point inside the shell
(d) none of these

## Paragraph Based Questions

(A) A thin rod of length L and mass M is placed along x axis.One end of rod is placed at origin and other end is at (L,0).
Let i and j are the unit vector across x and y axis
Question 3:
Find the Gravitational field at Point P( a,0) where a > L
(a) $\frac {GM}{a(L+a)}\mathbf{i}$
(b) $\frac {GM}{a(a-L)}\mathbf{i}$
(c) $\frac {GM}{L-a}\mathbf{i}$
(d ) None of these

Question 4
Find the gravitational potential at point P .We take gravitational potential to be zero at infinity
(a) $\frac {GM}{L} ln \frac {a+L}{a}$
(b) $\frac {GM}{L} ln \frac {a}{a -L}$
(c) $\frac {GM}{L} ln \frac {a-L}{a+L}$
(d) $\frac {GM}{L} ln \frac {a-L}{a}$

(B)Three particles A,B,C each of mass m are placed at the corner of the equilateral triangle of side a. Question 5
Find the potential energy of the system
(a) $- \frac {3Gm^2}{a}$
(a) $- \frac {3Gm^2}{2a}$
(a) $- \frac {Gm^2}{3a}$
(d) None of these

Question 6
Find the Gravitational Potential at point A
(a)$-\frac {2Gm}{a}$
(b)$-\frac {Gm}{a}$
(c) $-\frac {3Gm}{a}$
(d) None of these

Question 7
Find the work done on this system if the side of the triangle is changed from a to 3a
(a) $\frac {4Gm^2}{a}$
(b) $\frac {3Gm^2}{a}$
(c) $\frac {Gm^2}{a}$
(d) $\frac {2Gm^2}{a}$

## Multiple Choice Questions

Question 8
Three concentric shells A,B ,C of uniform density have masses M1 ,M2 and M3 respectively. There radii are R1,R2 and R3 respectively.
R3 > R2 > R1.
A particle of mass m is placed at placed at a distance d
Match the column
Column A ( it tells us about the location)
(P) R1 < d < R2
(Q) d < R1
(R) R1 < R2 < d < R3
(S) R1 < R2 < R3 < d
Column B ( it tells us about the gravitational force experienced)
(D) $\frac {G(M_1 + M_2 + M_3)m}{d^2}$
(E) $\frac {G(M_1 + M_2)m}{d^2}$
(F) $\frac {GM_1m}{d^2}$
(G) 0

Question 9
A satellite of mass m is orbiting the earth in a circular orbit of radius R.
Statement I: Angular Momentum of the satellite varies as $\frac {1}{\sqrt {R}}$
Statement II: Linear momentum of the satellite varies as 1/R
Statement III: Kinetic energy varies as 1/R
Statement IV: Frequency of revolution varies as $\frac {1}{R^{3/2}}$
Which of the following is correct
(a) All the statements are correct
(b) Statement I,II,III are correct only
(c) Statement II,IV are correct only
(d) Statement I,II,IV are correct only

Question 10
The force of gravitation is
(a) Repulsive
(b) Electrostatic
(c) Conservative
(d) Non-conservative

Question 11
Mass M is divided into two parts bM and (1-b)M. For a given separation, the value of b for which the gravitational attraction between the two pieces becomes maximum is
(a) 1/2
(b) 3/5
(c) 1
(d) 2

Question 12
A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of earth
(a) The acceleration of S is always directed towards the centre of the earth
(b) The angular momentum of S about the centre of the earth changes in direction but its magnitude remains constant
(c) The total mechanical energy of S varies periodically with time
(d) The linear momentum of S remains constant in magnitude

Question 13
A geostationary satellite orbits around the earth in a circular orbit of radius 36000 km. Then, the time period of a satellite orbiting a few hundred kilometres above the earth?s surface ($R_{Earth}=6400km$) will approximately be
(a) 1/2 h
(b) 1 h
(c) 2 h
(d) 4 h

Question 14
Which of the following options are correct?
(a) Acceleration due to gravity decreases with increasing altitude.
(b) Acceleration due to gravity increases with increasing depth (assume the earth to be a sphere of uniform density).
(c) Acceleration due to gravity increases with increasing latitude.
(d) Acceleration due to gravity is independent of the mass of the earth.

Question 15
Two bodies of masses $m_1$ and $m_2$ are initially at rest at infinite distance apart. They are then allowed to move towards each other under mutual gravitational attraction. Their relative velocity of approach at a separation distance r between them is
(a)$\sqrt {2G \frac {m_1 - m_2}{r}}$
(b)$\sqrt {2G \frac {m_1 + m_2}{r}}$
(c)$\sqrt {2G \frac {m_1 m_2}{r}}$
(d)$\sqrt {2G \frac {r}{m_1m_2}}$

Question 16
If the mass of sun were ten times smaller and gravitational constant G were ten times larger in magnitudes-
(a) walking on ground would became more difficult.
(b) the acceleration due to gravity on earth will not change.
(c) raindrops will fall much faster.
(d) airplanes will have to travel much faster

## Subjective Questions

Question 17
A cosmic body A of mass m moves to the sun with velocity v0 ( when far from sun) and aiming parameter d the arm of the velocity v0 relative to the center of the sun.
(a) Find the angular momentum of the body about the sun at the starting point
(b) Find the minimum distance which this body will get to the sun
(c) Find the velocity at minimum separation
(d) Find the total energy of the system at the minimum distance
Mass of the sun =Ms

Question 18
A planet of mass M moves along a ellipse around the sun so that its maximum and minimum distance from the sun are equal to a and b respectively
(a) Find the velocities at the minimum and maximum distance
(b) Find the Total energy of the system
(c) Find the angular momentum of the planet relative to the center of the sun
(d) At a point P when at a distance r0 from the sun,the angle between velocity vector and radius vector is θ. Find the velocity at the point P
(e) find the ecentricty and semi major axis of the ellipse
Mass of the sun =m

Question 19
A hole were drilled completely through the earth along a diameter.A particle of mass m is released into the hole from the surface of the earth
(a) find the force acting on the mass m at distance r from the center
(b) Show that the motion will be simple harmonic and Find out the time period of it
Let M be the mass of the Earth
R be the radii of the Earth
We assume that density is Uniform

Question 20
Two satellite M and N are revolving around the earth in coplanar concentric orbits.
The Time period of the satellite are 2 h and 16 H respectively. The radius of the orbit of the satellite N is 3.2X 104 Km.The satellite are moving in opposite direction.
At t=0, the position of the satellite is shown in below figure
Find out the following things
(a) The time period of the satellite M
(b) Orbital velocity of both the satellite
(c) Find the angular velocity of satellite N as observed by M at t=8 hour

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