Question

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

• A. 6m
• B. 2/9 m
• C. 2/3m
• D. 18m

Answer 1

Answer: (D)

It is given that acceleration due to gravity on plane. A is 9 times the acceleration due to gravity on planet B i.e.,
$ {{g}_{A}}=9{{g}_{B}} $ ..(i)
From third equation of motion $ {{v}^{2}}=2gh $
At planet $ A,{{h}_{A}}=\frac{{{v}^{2}}}{2{{g}_{A}}} $ ...(ii)
At planet $ S,{{H}_{B}}=\frac{{{v}^{2}}}{2{{g}_{B}}} $ ...(iii)
Dividing Eq. (ii) by Eq. (iii) we have
$ \frac{{{h}_{A}}}{{{h}_{B}}}=\frac{9{{g}_{B}}}{{{g}_{A}}} $
From Eq. (i), $ {{g}_{A}}=9{{g}_{B}} $
$ \therefore $ $ \frac{{{h}_{A}}}{{{h}_{B}}}=\frac{{{g}_{B}}}{9{{g}_{B}}}=\frac{1}{9} $
or $ {{h}_{B}}=9{{h}_{B}}=9\times 2=18\,m $
$ (\therefore {{h}_{A}}=2m) $