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^-10 J

D.

6.67 x10^-10 J

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

• 0.11 kms⁻¹

C.

110 kms⁻¹

A satellite is revolving in a circular orbit at a height ‘h’ from the earth’s surface (radius of earth R ; h<<R). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth’s gravitational field, is close to: (Neglect the effect of atmosphere.)

• 
• 
• 
• 

D.

Given, a satellite is revolving in a circular orbit at a height h from the Earth's surface having radius of earth R, i.e h <<R
Orbit velocity of a satellite

therefore, the minimum increase in its orbital velocity required to escape from the Earth's Gravitational Field.

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

• 
• 

D.

The gravitational force exerted on satellite at a height x is

where Me = mass of earth Since, gravitational force provides the necessary centripetal force, so,

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

• rotational kinetic energy