Question

Consider another planet which has mas, M = 2 Mearth and radius, r = rearth / 2. If you are at
that planet to test its ground and now, you would like to come back to Earth, what should be
your escape speed compared to Earth’s escape speed? (3)
(C) An object has length L, area A and volume V. write down the stress vs strain for L, A and
V relation. (2 marks)

Answer 1

The escape velocity of the Earth and that planet:

$$v=\sqrt{\frac{2GM}{R}},\\\space\\ u=\sqrt{\frac{8GM}{R}}=2v.$$

The escape velocity should be two times greater.

(C) Obtain the stress-strain relation.

$$\sigma=\frac FA=\frac{FL}{V}.\\\space\\ \epsilon=\frac{\Delta L}{L}=\frac{\Delta LA}{V}.\\\space\\ \sigma(\epsilon)=\frac{FL}{\Delta LA}\epsilon.$$