A mass falls from a height ' 
' and its time of fall ' 
' is recorded in terms of time period 
of a simple pendulum. On the surface of earth, it is found that 
. The entire set up is taken on the surface of another planet whose mass is half of earth and radius the same. Same experiment is repeated and corresponding times noted as 
and 
. [NEET 2019]
Text Solution
Verified by ExpertsD
Time of fall 
is given by 
… (i)
The time period of simple pendulum is
… (ii)
where, 
is the length of the pendulum. From Eqs. (i) and (ii), since 
and 
are constants, so we can conclude that
Thus, the ratio of time of fall and time period of pendulum is independent of value of gravity ( 
) or any other parameter like mass and radius of the planet. Thus, the relation between 
and 
on another planet irrespective of its mass or radius will remains same as it was on earth, i.e.
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