SATHEE: Gravitation - Result Question 20

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) $\frac{2}{9} m$

(d) $6 m$

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Answer:

Correct Answer: 20. (c)

Solution:

$\begin{aligned} \frac{1}{2} m v^{2} = m g_{A} h_{A} = m g_{B} h_{B} \\ \Rightarrow g_{A} h_{A} = g_{B} h_{B} \end{aligned}$

$\Rightarrow h_{B} = (\frac{g_{A}}{g_{B}}) h_{A} = 9 \times 2 = 18 m$

The velocity of the mass while reaching the surface of both the planets will be same.

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

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

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

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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 2m on the surface of A. What is the height of jump by the same person on the planet B ?

Answer:

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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 $B$ ?