Question

A body is dropped from some height and it falls through a distance d in a certain time on the earth, then if the same body is dropped on another planet having mass and radius twice as that of the earth, the distance through which it falls in the same time is (considering acceleration due to gravity to be constant over small altitude) (A) d2 (B) 2 d (C) 4 d (D) d

Answer 1

Answer:

If the body is dropped in earth's gravitational field, d is the distance travelled in time t , then we have

 

d = (1/2) g t2 ...............(1)

 

where g is acceleration due to gravity in earth's gravitational field .

 

If the body is dropped in some other planet's gravitational field, d' is the distance travelled in time t , then we have

 

d' = (1/2) g' t2 ................(2)

 

where g' is acceleration due to gravity in other planet's gravitational field

 

By dividing eqn.(2) by eqn.(1), we get,  d'/d = g'/g  ........................(3)

 

we have, acceleration due to gravity on earth,  g  = GM/R2 .......................(4)

 

where G is universal gravitation constant, M is mass of earth and R is radius of earth

 

we have, acceleration due to gravity on other planet,  g'  = G(2M)/(2R)2 = (1/2) GM/R2 .......................(5)

 

Hence, from eqn.(4) and (5), we get,  g'/g = (1/2) .....................(6)

 

using eqns.(3) and (6), we get d'/d = (1/2)   or  d' = d/2