First slide

Gravitational potential and potential energy

Question

A person can jump to a height of 3m on the earth on a planet of density $\frac{1}{3}$ rd that of the earth and radius $\frac{1}{2}$ of the earth, he can jump to a height of

Easy

A

2m
B

10m
C

18m
D

8m

Solution

$\begin{array}{l} P E_{e} = P E_{p} \\ \Rightarrow m g_{e} h_{e} = m g_{p} h_{p} \\ h_{P} = \frac{g_{e} h_{e}}{g_{p}} - - - (1) \\ g = \frac{4}{3} π G R ρ \\ \frac{g_{e}}{g_{p}} = \frac{R_{e}}{R_{p}} \frac{ρ_{e}}{ρ_{p}} = \frac{R_{e}}{\frac{R_{e}}{2}} \frac{ρ_{e}}{\frac{ρ_{e}}{3}} = 6 - - - - (2) \\ s u b s t i t u t e i n (1) \\ h_{P} = \frac{g_{e} h_{e}}{g_{p}} = 6 \times 3 = 18 m \end{array}$

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