Gravitation Ques 17
17. 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 $B$ ?
[2003]
(a) $\frac{2}{3}$ $ m$
(b) $\frac{2}{9}$ $ m$
(c) $18$ $ m$
(d) $6$ $ m$
Show Answer
Answer:
Correct Answer: 17.(c)
Solution:
- (c) Applying conservation of total mechanical energy principle
$ \begin{aligned} & \frac{1}{2} m v^{2}=m g_A h_A=m g_B h_B \\ & \Rightarrow g_A h_A=g_B h_B \end{aligned} $
$\Rightarrow h_B=(\frac{g_A}{g_B}) h_A=9 \times 2=18 $ $m$
The velocity of the mass while reaching the surface of both the planets will be same.
$\Rightarrow \sqrt{2 g^{\prime} h^{\prime}}=\sqrt{2 g h}$
$\Rightarrow \sqrt{2 g h^{\prime}}=\sqrt{2 \times 9 g \times 2}$
$\Rightarrow 2 h^{\prime}=36 \Rightarrow h^{\prime}=18 $ $m$
BETA
