Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

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?

18 m

6 m

2/3 m

2/9 m

Step-by-Step Solution

Identify the Principle: The height $H$ reached by a person jumping vertically depends on the initial velocity $u$ (supplied by the person's energy) and the acceleration due to gravity $g$ . Using the kinematic equation $v^2 = u^2 - 2gH$ (where final velocity $v=0$ at max height), we get: $H = \frac{u^2}{2g}$
Analyze the Relationship: Assuming the person exerts the same effort, the initial velocity $u$ remains constant on both planets. Therefore, the height reached is inversely proportional to gravity ( $H \propto \frac{1}{g}$ ). $H_A g_A = H_B g_B$
Substitute Values:

Given: $g_A = 9 g_B$ and $H_A = 2 \text{ m}$ .
Substitute into the equation: $2 \times (9 g_B) = H_B \times g_B$ $18 g_B = H_B g_B$ $H_B = 18 \text{ m}$ .

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