A person is standing in an elevator. In which situation he finds himself weightless?

• Elevator is going up with constant speed.

• Elevator is moving down with constant speed.

• Elevator is accelerating up with g.

• Elevator is accelerating down with g.

A satellite is in an orbit around the earth. If its kinetic energy is doubled, then

• it will maintain its path

• it will fall on the earth

• it will rotate with a great speed

• it will escape out of earth's gravitational field

What will be the effect on the weight of a body placed on the surface of earth, if earth suddenly ' stops rotating?

• No effect

• Weight will increase

• Weight will decrease

• Weight will become zero

Gravitational potential of the body of mass m at a height h from surface of earth of radius R is (Take g = acceleration due to gravity at earth's surface)

• - g(R + h )

• - g ( R + h )

• g  ( R + H )

• g ( R - h )

A body of mass 'm' is taken from the earth's surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be

• 3mgR

• $\frac{1}{3} \mathrm{mgR}$

• 2 mgR

• $\frac{2}{3} \mathrm{mgR}$

Find out the correct relation for the dependance of change in acceleration due to gravity on the angle at the latitude, due to rotation of earth

• dg ∝ cos$\mathrm{\varphi }$

• dg ∝ cos²$\mathrm{\varphi }$

• dg ∝ cos^3/2$\mathrm{\varphi }$

• dg ∝ $\frac{1}{\mathrm{cos\varphi }}$

Assertion: Total energy is conserved in moving a satellite to higher orbit. 

Reason:  Sum of change in PE and KE is same in magnitude and opposite in nature.

• If both assertion and reason are true and reason is correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion

• If assertion is true but reason is false.

• If both assertion and reason are false.

Assertion:  The difference in the value of acceleration due to gravity at pole and equator is proportional to square of angular velocity of earth. 

Reason:  The value of acceleration due to gravity is minimum at the equator and maximum at the pole.

• If both assertion and reason are true and reason is the correct explanation of assertion

• If both assertion and reason are true but reason is not the correct explanation of assertion

• If assertion is true but reason is false

• If both assertion and reason are false.

A  wire  of  length  l and  mass  m  is  bent  in the  form of  a  semicircle. The   gravitational  field  intensity  at the  centre  of  semicircle  is

• $\frac{\mathrm{G} \mathrm{m}}{\mathrm{\pi } \mathrm{l}}$ along x - axis

• $\frac{\mathrm{G} \mathrm{m}}{\mathrm{\pi } \mathrm{l}}$ along y-axis

• $\frac{2\mathrm{\pi } \mathrm{G} \mathrm{m}}{{\mathrm{l}}^2}$ along y-axis

• $\frac{2 \mathrm{\pi } \mathrm{G} \mathrm{m}}{{\mathrm{l}}^2}$ along x-axis

Suppose  the gravitational  force varies inversely as the  n^th  power of distance. Then the time period of a planet in circular orbit of radius R around the sun will be proportional to

• ${\mathrm{R}}^{\left(\frac{\mathrm{n} + 1}{2}\right)}$

• ${\mathrm{R}}^{\left(\frac{\mathrm{n} - 1}{2}\right)}$

• Rⁿ

• ${\mathrm{R}}^{\left(\frac{\mathrm{n} - 2}{2}\right)}$