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1.

The distance of a planet from the sun is \(5\) times the distance between the earth and the sun. The time period of the planet is: 

1.	\(5^{3/2}\) years	2.	\(5^{2/3}\) years
3.	\(5^{1/3}\) years	4.	\(5^{1/2}\) years

2.

Two spheres of masses \(m\) and \(M\) are situated in air and the gravitational force between them is \(F.\) If the space around the masses is filled with a liquid of specific density \(3,\) the gravitational force will become:
1. \(3F\)
2. \(F\)
3. \(F/3\)
4. \(F/9\)

3. What is the depth at which the value of acceleration due to gravity becomes \(\dfrac{1}{{n}}\) times it's value at the surface of the earth? (radius of the earth = \(\mathrm{R}\))  

1.	\(\dfrac R {n^2}\)	2.	\(\dfrac {R~(n-1)} n\)
3.	\(\dfrac {Rn} { (n-1)}\)	4.	\(\dfrac R n\)

4. A particle is released from a height of \(S\) above the surface of the earth. At a certain height, its kinetic energy is three times its potential energy. The distance from the earth's surface and the speed of the particle at that instant are respectively:

1.	\(\frac{S}{2},\frac{\sqrt{3gS}}{2}\)	2.	\(\frac{S}{4}, \sqrt{\frac{3gS}{2}}\)
3.	\(\frac{S}{4},\frac{3gS}{2}\)	4.	\(\frac{S}{4},\frac{\sqrt{3gS}}{3}\)

5.

If the radius of a planet is \(R\) and its density is \(\rho,\) the escape velocity from its surface will be:
1. \(v_e\propto \rho R\)
2. \(v_e\propto \sqrt{\rho} R\)
3. \(v_e\propto \frac{\sqrt{\rho}}{R}\)
4. \(v_e\propto \frac{1}{\sqrt{\rho} R}\)

6. Given below are two statements: 

Assertion (A):	The orbit of a satellite lies within Earth's gravitational field, while escaping occurs beyond the Earth's gravitational field.
Reason (R):	The orbital velocity of a satellite is greater than its escape velocity.

 

1.	Both (A) and (R) are True and (R) is the correct explanation of (A).
2.	Both (A) and (R) are True but (R) is not the correct explanation of (A).
3.	(A) is True but (R) is False.
4.	Both (A) and (R) are False.

7.

Starting from the centre of the earth, having radius \(R,\) the variation of \(g\) (acceleration due to gravity) is shown by:

1.		2.
3.		4.

8.

Mass \(M\) is divided into two parts \(xM\) and \((1-x)M.\) For a given separation, the value of \(x\) for which the gravitational attraction between the two pieces becomes maximum is:

1.	\(\frac{1}{2}\)	2.	\(\frac{3}{5}\)
3.	\(1\)	4.	\(2\)

9.

A particle starts from rest at a large distance from a planet, reaches the planet solely under gravitational attraction, and passes through a smooth tunnel through its center. Which statement about the particle is/are correct?

1.	The total energy of the particle will be zero at a large distance.
2.	The gravitational potential energy of the particle at the centre will be \(\frac{3}{2}\) times that of at the surface of the planet.
3.	The gravitational potential energy of the particle at the centre of the plant will be zero.
4.	Both statements (1) and (2) are correct.

10.

A planet moves around the sun. At a point \(P,\) it is closest to the sun at a distance \(d_1\) and has speed \(v_1.\) At another point \(Q,\) when it is farthest from the sun at distance \(d_2,\) its speed will be:

1.	\(\dfrac{d_2v_1}{d_1}\)	2.	\(\dfrac{d_1v_1}{d_2}\)
3.	\(\dfrac{d_1^2v_1}{d_2}\)	4.	\(\dfrac{d_2^2v_1}{d_1}\)