The acceleration due to gravity on the planet `A` is `9` times the acceleration due to gravity on planet `B`. A man jumps to a height of `2 m` on the surface of `A`. What is the height of jump by the same person on the planet `B` ?

Options

A. 6m
B. `(2)/(3)m`
C. `2//9`m
D. 18m

Answer

D

Explanation

It is given that, acceleration due to gravity on planet A is 9 times the acceleration due to gravity on planet ie,
`g_(A)=9_(g_(B)).....(i)`
For third equation of motion
`v^(2)=2gh`
At plaenet A, `h_(A)=(v^(2))/(2g_(A)),......(ii)`
At plaenet B, `h_(B)=(v^(2))/(2g_(B))......(iii)`
Dividing Eq. (ii) by Eq. (iii), we have
`(h_(A))/(h_(B))=(g_(B))/(g_(A))`
From Eq. (i) `g_(A)=9g_(B)`
`therefore (h_(A))/(h_(B))=(g_(B))/(9g_(B))=(1)/(9)`
or `h_(B)=9h_(A)=9xx2=18m (therefore h_(A)=2m)`