Question

A man can jump 1.5 m high on the earth. Calculate the approximate height he might be able to jump on a palnet whose density is one-quarter that of earth and whose radius is one-third of the earth’s radius?
1. 1.5 m
2. 12 m
3. 18 m
4. None

Answer 1

Correct Answer - Option 3 : 18 m

Acceleration due to gravity on the earth’s surface, \(g = \frac{4}{3}\pi GR\rho\)

On the planet, \(g' = \frac{4}{3}\pi GR'\rho ' = \frac{4}{3}\pi G \times \frac{R}{3} \times \frac{\rho }{4} = \frac{1}{{12}}g\;\)

Assuming that the man puts same energy in jumping on earth and the planet,

\(mgh = mg'h' \Rightarrow gh = \frac{g}{{12}} \times h' \)

\(\Rightarrow h' = 12h = 12 \times 1.5 = 18\;m\;\)