Question

A man can jump to a height of 1.5 m on a planet A. What is the height he may be able to jump on another planet whose density and radius are, respectively, one-quarter and one-third that of planet A

• A. 1.5 m
• B. 15 m
• C. 18 m
• D. 28 m

Answer 1

Answer: (C)

18 m

Answer 2

$H = \frac { u ^ { 2 } } { 2 g } \Rightarrow H \propto \frac { 1 } { g }$ ⇒ $\frac { H _ { B } } { H _ { A } } = \frac { g _ { A } } { g _ { B } }$

Now $g _ { B } = \frac { g _ { A } } { 12 }$ as $g \propto \rho R$

∴$\frac { H _ { B } } { H _ { A } } = \frac { g _ { A } } { g _ { B } }$=12⇒ $H _ { B } = 12 \times H _ { A } = 12 \times 1.5 = 18 \mathrm {~m}$