The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M, to transfer it from a circular orbit of radius R₁ to another of radius R₂(R₂> R₁) is 

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• 
• 
• 

D.

The kinetic energy changing the orbit of satellite

The speed of the projectile at its maximum height is half of its initial speed. The angle of projection is

• 60^o

• 15^o

• 30^o

• 45^o

From a circular disc of radius R and mass 9M, a small disc of mass M and radius R/3 is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre is

• 40MR²/9

• MR²

• 4 MR²

• 4MR²/9

A particle moves in the x-y plane according to rule x = a sin ωt and y = a cos ωt. The particle follows

• an elliptical path

• a circular path 

• a parabolic path

• a straight line path inclined equally to x and y- axes

B.

a circular path 

This is the equation of a circle, so the particle follows a circular path.

A closely wound solenoid of 2000 turns and area of cross -section 1.5 x 10^-4 m² carries a current of 2.0 A. It is suspended through its centre and perpendicular to its length, allowing it to turn in a horizontal plane in a uniform magnetic field 5 x 10^-2 T making an angle of 30^o with axis of  the solenoid. The torque on the solenoid will be

• 3 x 10^-3 N-m

• 1.5 x 10^-3 N-m

• 1.5 x 10^-2 N-m

• 3 x 10^-2 N-m