A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11 kms⁻¹, the escape velocity from the

• 1.1 kms⁻¹

• 11 kms⁻¹

• 110 kms⁻¹

• 110 kms⁻¹

This question contains Statement -1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement – I:
For a mass M kept at the centre of a cube of side ‘a’, the flux of gravitational field passing through its sides is 4π GM.
and
Statement – II
If the direction of a field due to a point source is radial and its dependence on the distance ‘r’ for the source is given as 1/r₂, its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface

• Statement – 1is false, Statement – 2 is true.

• Statement – 1is true, Statement – 2 is true; Statement -2 is correct explanation for Statement-1.

• Statement – 1 is true, Statement – 2 is true; Statement -2 is not a correct explanation for Statement-1.

• Statement – 1 is true, Statement – 2 is true; Statement -2 is not a correct explanation for Statement-1.

If g_E and g_m are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan’s oil drop experiment could be performed on the two surfaces, one will find the ratio (electronic charge on the moon/ electronic charge on the earth) to be

• 1

• 0

• g_E/g_M

• g_E/g_M

Average density of the earth

• does not depend on g

• is a complex function of g

• is directly proportional to g

• is directly proportional to g

The change in the value of g at a height ‘h’ above the surface of the earth is the same as at a depth ‘d’ below the surface of earth. When both ‘d’ and ‘h’ are much smaller than the radius of earth, then which one of the following is correct?

• d =h/2

• d=3h/2

• d =2h

• d =2h

A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force between
(you may take G = 6 . 67× 10^-11 Nm²/ kg²)

• 13.34 x 10^-10 J

• 3.33 x 10^-10 J

• 6.67 x10^-9 J

• 6.67 x10^-9 J

A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following will not be affected?

• moment of inertia

• angular momentum

• angular velocity

• angular velocity

18.

A satellite of mass m revolves around the earth of radius R at a height x from its surface. If g is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

• 

• gx

• 
• 

The time period of an earth satellite in circular orbit is independent of

• the mass of the satellite

• radius of its orbit

• both the mass and radius of the orbit

• both the mass and radius of the orbit

If g is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of object of mass m raised from the surface of the earth to a height equal to the radius R of the earth is

• 2 mgR

• mgR/2

• mgR/4

• mgR/4