G R AV I TAT I O N

Q.25 A satellite of mass m is launched vertically upwards with an initial speed u from the surface of the earth.

m
After it reaches height R (R = radius of the earth), it ejects a rocket of mass so that subsequently
10
the satellite moves in a circular orbit. The kinetic energy of the rocket is (G is the gravitational constant;
M is the mass of the earth) [JEE MAIN 2020]
2
3m  5GM  m  2 113 GM 
u   u 
20  200 R 
(1) (2)
8  6R 

2
m 2GM   119GM 
u   5m  u2 
200R 
(3) (4)
20  3R  

Q.26 A box weighs 196 N on a spring balance at the north pole. Its weight recorded on the same
balance if it is shifted to the equator is close to (Take g = 10 ms–2 at the north pole and the
radius of the earth = 6400 km) : [JEE MAIN 2020]
(1) 195.32 N (2) 194.32 N (3) 194.66 N (4) 195.66 N
Q.27 Consider two solid spheres of a radii R1  1m, R 2  2m and masses M1 amd M2, respectively..
M1
The gravitational field due to sphere (1) and (2) are shown. The value of M is :
2

[JEE MAIN 2020]

1 1 1 2
(1) (2) (3) (4)
6 3 2 3
Q.28 An asteroid is moving directly towards the centre of the earth. When at a distance of 10 R (R
is the radius of the earth) from the earths centre, it has a speed of 12 km/s. Neglecting the
effect of earths atmosphere, what will be the speed of the asteroid when it hits the surface
of the earth (escape velocity from the earth is 11.2 km/s)? Give your answer to the nearest
integer in kilometer/s .................. [JEE MAIN 2020]

Q.29 Planet A has mass M and radius R, Planet B has half the mass and half the radius of planet A.
vA n
If the escape velocities from the planets A and B are va and vB, respectively, then v  4 ,
B

The value of n is : [JEE MAIN 2020]

(1) 1 (2) 3 (3) 2 (4) 4

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K
Q.30 The mass density of a spherical galaxy varies as over a large distance ‘r’ from its centre. In that
r
region, a small star is in a circular orbit of radius R. Then the period of revolution, T depends on R as :
[JEE MAIN 2020]
1
(2) T 
2
(1) T  R (3) T2  R (4) T2  R3
R3
Q.31 The height ‘h’ at which the weight of a body will be the same as that at the same depth ‘h’ from the
surface of the earth is (Radius of the earth is R and effect of the rotation of the earth is neglected)
[JEE MAIN 2020]

5R – R 5 3R – R
(1) (2) R–R (3) R/2 (4)
2 2 2
Q.32 A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the
earth’s radius Re. By firing rockets attached to it, its speed is instantaneously increased in the direction of
3
its motion so that it become times larger. Due to this the farthest distance from the centre of the
2
earth that the satellite reaches is R. Value of R is : [JEE MAIN 2020]
(1) 4Re (2) 3Re (3) 2Re (4) 2.5Re

 r2 
Q.33 The mass density of a planet of radius R varies with the distance r from its centre as ρ(r)  ρ 
0 1  
2 .
 R 
Then the gravitational field is maximum at : [JEE MAIN 2020]

1 5 3
(1) r  R (2) r  R (3) r  R (4) r = R
3 9 4
Q.34 On the x-axis and a distance x from origin, the gravitational field due to a mass distribution is given by
Ax
x 2
 a2 
3/ 2 in the x-direction. The magnitude of gravitational potential on the x-axis at a distance x,

taking its value to be zero at infinity, is : [JEE MAIN 2020]

A A
(1)
x 2
a 
2 1/ 2 (2)
x 2
 a2 
3/ 2 (3) A(x2 + a2)3/2 (4) A(x2 + a2)1/2

Q.35 A body is moving in a low circular orbit about a planet of mass M and radius R. The radius of the orbit
can be taken to be R itself. Then the ratio of the speed of this body in the orbit to the escape velocity
from the planet is : [JEE MAIN 2020]
1
(1) 1 (2) 2 (3) (4) 2
2

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R
Q.36 The value of the acceleration due to gravity is g1 at a height h = (R = radius of the earth) from the
2
d
surface of the earth. It is again equal to g1 at a depth d below the surface of the earth. The ratio  
R
equals : [JEE MAIN 2020]
7 4 1 5
(1) (2) (3) (4)
9 9 3 9
Q.37 The acceleration due to gravity on the earth’s surface at the poles is g and angular velocity of the earth
about the axis passing through the pole is . An object is weighed at the equator and at a height h above
the poles by using a spring balance. If the weights are found to be same, then h is : (h << R, where R is
the radius of the earth) [JEE MAIN 2020]

R 2ω2 R 2ω2 R 2ω2 R 2ω2

(1) (2) (3) (4)
8g 4g g 2g
Q.38 A satellite is in an elliptical orbit around a planet P. It is observed that the velocity of the satellite when it
is farthest from the planet is 6 times less than that when it is closest to the planet. The ratio of distances
between the satellite and the planet at closest and farthest points is : [JEE MAIN 2020]
(1) 1 : 6 (2) 3 : 4 (3) 1 : 3 (4) 1 : 2
Q.39 Two planets have masses M and 16 M and their radii are a and 2a, reapectively. The separation between
the centres of the planets is 10a. A body of mass m is fired from the surface of the larger planet towards
the smaller planet along the line joining their centres. For the body to be able reach at the surface of
smaller planet, the minimum firing speed needed is : [JEE MAIN 2020]

GM 2 3 5GM GM GM
(1) (2) (3) 4 (4) 2
ma 2 a a a

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