Height of jump on different planets – Rankers Physics
Topic: Gravitation
Subtopic: Acceleration Due to Gravity and its variation

Height of jump on different planets

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 $2\text{ m}$ on the surface of $A$. What is the height of jump by the same person on the planet $B$:

(2003)

$\frac{2}{9}\text{ m}$
$18\text{ m}$
$6\text{ m}$
$\frac{2}{3}\text{ m}$

Solution:

The muscular work done in jumping is the same, so the potential energy gained is constant: $m g_A h_A = m g_B h_B$. Substituting $g_A = 9 g_B$ and $h_A = 2\text{ m}$, we get $9 g_B \times 2 = g_B \times h_B \implies h_B = 18\text{ m}$.

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