Amity International School,Pushp Vihar

UNIT TEST III SET - B

Class 11 - Physics
Time Allowed: 1 hour and 10 minutes Maximum Marks: 30

Section A
1. A body of weight 72 N moves from the surface of earth at a height half of the radius of earth, then gravitational [1]
force exerted on it will be:

a) 36 N b) 144 N

c) 50 N d) 32 N
2. If the radius of earth decreases by 1% and its mass remains same, then the acceleration due to gravity. [1]

a) decreases by 2% b) increases by 1%

c) decreases by 1% d) increases by 2%
3. The value of acceleration due to gravity g at distance r from earth's centre such that r < R depends on r according [1]
to relation (R = radius of earth):

a) g ∝ r b) g ∝
1

c) g ∝ 1
2
d) g ∝ r
2

4. The direction of the universal gravitational force between particles of masses m and m is:
1 2 [1]

a) towards m 1 b) towards m2 on m1 and towards m on m

1 2

c) towards the center of the earth d) towards m 2

5. Assertion (A): When the distance between two bodies is doubled and also a mass of each body is also doubled, [1]
the gravitational force between them remains the same.
Reason (R): According to Newton's law of gravitation, force is directly proportional to the mass of bodies and
inversely proportional to the distance between them.

a) Both A and R are true and R is the correct b) Both A and R are true but R is not the
explanation of A. correct explanation of A.

c) A is true but R is false. d) A is false but R is true.

6. Assertion (A): A body becomes weightless at the centre of earth. [1]
Reason (R): As the distance from centre of earth decreases, acceleration due to gravity increases.

a) Both A and R are true and R is the correct b) Both A and R are true but R is not the
explanation of A. correct explanation of A.

c) A is true but R is false. d) A is false but R is true.

Section B
7. Two planets of radii r1, and r2 are made from the same material. Calculate the ratio of the acceleration due to [2]

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 gravity on the surface of the planets.
OR
A man can jump 1.5 m high on earth. Calculate the height he may be able to jump on a planet whose density is one
fourth that of the earth and Whose radius is one-third of the earth.
8. How much below the surface of the earth does the acceleration due to gravity [2]
i. reduces to 36%
ii. reduces by 36% of its value on the surface of the earth? Radius of the earth = 6400 km.
9. Calculate the energy required to move a body of mass m from an orbit of radius 2R to 3R. [2]
Section C
10. Two heavy spheres each of mass 100 kg and radius 0.1 m are placed 10 m apart on a horizontal table. What is [3]
the gravitational field and potential at the midpoint of the line joining the centres of the spheres? Take G = 6.67
× 10-11 Nm2 kg-2.
11. What do you mean by gravitational potential energy of a body? Obtain an expression for it for a body of mass m [3]
lying at distance r from the centre of the earth. Hence write the expression for gravitational potential.
12. The planet Mars has two moons, Phobos and Deimos. [3]

a. Phobos has a period 7h, 39 min and an orbital radius of 9.4 × 103 km. Calculate the mass of mars.
b. Assume that earth and mars move in circular orbits around the sun with the Martian orbit being 1.52
times the orbital radius of the earth. What is the length of the Martian year in days? [ Use (1.52)3/2 = 1.83]
OR
Two uniform solid spheres of equal radii R, but mass M and 4M have a centre to centre separation 6R, as shown in
Fig. The two spheres are held fixed. A projectile of mass m is projected from the surface of the sphere of mass M
directly towards the centre of the second sphere. Obtain an expression for the minimum speed v of the projectile so
that it reaches the surface of the second sphere.

Section D
13. Read the text carefully and answer the questions: [4]
The figure shows the schematic drawing of Cavendish's experiment to determine the value of the gravitational
constant. The bar AB has two small lead spheres attached at its ends. The bar is suspended from a rigid support
by a fine wire. Two large lead spheres are brought close to the small ones but on opposite sides as shown. The
name of G from this experiment came to be

6.67 × 10-11 N-m2/kg2

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 (a) The big spheres attract the nearby small ones by a force which is

a) equal but in same direction b) equal and opposite

c) equal but in different direction d) unequal and opposite

(b) The net force on the bar is

a) Data insufficient b) zero

c) Data inadequate d) non-zero

(c) The net torque on the bar is

a) non-zero b) Both zero and non-zero

c) zero d) F times the length of the bar, where F is

the force of attraction between a big
sphere and its neighbouring
(d) The torque produces twist in the suspended wire. The twisting stops when

a) restoring torque of the wire b) restoring torque of the wire equals

limit the gravitational torque the gravitational torque

c) restoring torque of the wire exceeds d) The gravitational torque exceeds the
the gravitational torque restoring torque of the wire
Section E
14. The distance between the centers of two stars is 10a. The masses of these stars are M and 16 M and their radii a [5]
and 2a respectively. A body of mass m is fired straight from the surface of the larger star towards the smaller
star. What should be its minimum initial speed to reach the surface of the smaller star? Obtain the expression in
terms of G, M and a.
OR
Obtain an expression for the acceleration due to gravity on the surface of the earth in terms of mass of the earth and
its radius. Discuss the variation of acceleration due to gravity with altitude and depth. If a body is taken to a height R

from the surface of the earth, find percentage decrease in the weight of the body? Here R is the radius of the earth.

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