Question

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 $B$.

• A. 6 m
• B. 2/3 m
• C. 2/9 m
• D. 18 m

Answer 1

Answer: (D)

18 m

Answer 2

It is given that, acceleration due to gravity on plane $A$ is $9$ times the acceleration due to gravity on planet B ie,
$g_A=9g_B$ .......(i)
From third equation of motion
$v^2=2gh$
At planet A, $h_{A}=\frac{v^2}{2g_{A}}$ ......(ii)
At planet B, $h_{B}=\frac{v^2}{2g_{B}}$ ......(iii)
Dividing E (ii) by E (iii), we have
$\frac{h_{A}}{h_{B}}=\frac{g_{B}}{g_{A}}$
From E (i), $g_A = 9\,g_B$
= $\frac{h_{A}}{h_{B}}=\frac{g_{B}}{9g_{B}}=\frac{1}{9}$
or $h_B=9\,h_{A}$
$=9\times2\,=18\,m$
$(\therefore=h_{A}=2\,m)$AC