Gravitation - Result Question 20

20. 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) $6 m$

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Answer:

Correct Answer: 20. (c)

Solution:

  1. (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.

$\Rightarrow \sqrt{2 g^{\prime} h^{\prime}}=\sqrt{2 g h}$

$\Rightarrow \sqrt{2 g h^{\prime}}=\sqrt{2 \times 9 g \times 2}$

$\Rightarrow 2 h^{\prime}=36 \Rightarrow h^{\prime}=18 m$