The acceleration due to gravity on the planet A is 9 times the acceleration due to gravity on the 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?

Question

The acceleration due to gravity on the planet A is 9 times the acceleration due to gravity on the 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? (A) 6m (B) 2/9 m (C) 2/3m (D) 18m

Tardigrade Admin · Accepted Answer

It is given that acceleration due to gravity on plane. A is 9 times the acceleration due to gravity on planet B i.e.,

g_{A} = 9 g_{B}

..(i)
From third equation of motion

v^{2} = 2 g h

At planet

A, h_{A} = \frac{v ^{2}}{2 g _{A}}

...(ii)
At planet

S, H_{B} = \frac{v ^{2}}{2 g _{B}}

...(iii)
Dividing Eq. (ii) by Eq. (iii) we have

\frac{h _{A}}{h _{B}} = \frac{9 g _{B}}{g _{A}}

From Eq. (i),

g_{A} = 9 g_{B}

∴

\frac{h _{A}}{h _{B}} = \frac{g _{B}}{9 g _{B}} = \frac{1}{9}

or

h_{B} = 9 h_{B} = 9 \times 2 = 18 m

(∴ h_{A} = 2 m)

Q. The acceleration due to gravity on the planet A is 9 times the acceleration due to gravity on the 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?

6m

2/9 m

2/3m

18m