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Q)A body falls through a distance d in a certain time on earth . Then if the same body is related on another planet having mass and radius twice as that of earth , the distance through which it falls in the same time is ?(considering acceleration due to gravity to be constant over small altitude) A)d/2 B)2d C)4d D)d
Asked by shangamer2227 | 10 Oct, 2019, 07:30: PM
answered-by-expert Expert 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
 
 
Answered by Thiyagarajan K | 11 Oct, 2019, 08:16: AM

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