The height at which the weight of a body becomes 1/16th, its weight on the surface of earth (radius R), is

• 5R

• 15 R

• 3R

• 3R

A geostationary satellite is orbiting the earth at a height of 5R above that surface of the earth, R being the radius of the earth. The  time period of another satellite in hours at a height of 2R from the surface of the earth is

• 5

• 10

• 
• 

A spherical planet has a mass M_p and diameter D_p. A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity, equal to

• 4GM_p/D_p²

• GM_pm/D_p²

• GM_pm/ D_p²

• GM_pm/ D_p²

94.

An alternating electric field of frequency v is applied across the dees (radius =R ) of a cyclotron that is being used to accelerate protons (mass = m). The operating magnetic field (B) used in the cyclotron and the kinetic energy (K) of the proton beam, produced by it are given by

• 
• 
• 
• 

Infinite number of bodies, each of mass 2 kg are situated on x-axis at distance 1m, 2 m, 4 m, 8 m, respectively from the origin. The resulting gravitational potential due to this system at the origin will be

• -G

• 
• 
• 

A body projected vertically from the earth reaches a height equal to earth's radius before returning to the earth. The power exerted by the gravitational force is greatest

• at the instant just before the body hits the earth

• it remains constant all through

• at the instant just after the body is projected

• at the instant just after the body is projected

A boy standing at the t op of a tower of 20 m height drops a stone. Assuming g = 10 ms^-2, the velocity with which it hits the ground is 

• 20 m/s

• 40 m/s

• 5 m/s

• 5 m/s

A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small as compared to the mass of the earth. Then,

• the angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant

• the total mechanical energy of S varies periodically with time

• the linear momentum of S remains constant in magnitude

• the linear momentum of S remains constant in magnitude

A remote sensing satellite of earth revolves in a circular orbit at a height of 0.25 x 10⁶ m above the surface of the earth. if earth 's radius is 6.38 x 10⁶ m and g = 9.8 ms^-2 then the orbital speed of the  satellite is 

• 7.76 kms^-1

• 8.56 kms^-1

• 9.13 kms^-1

• 9.13 kms^-1

A particle of mass m is thrown upwards from the surface of the earth, with a velocity u. The mass and the radius of the earth are, respectively, M and R.G are gravitational constant and g is acceleration due to gravity on the surface of the earth. The minimum value of u so that the particle does not return back to earth is