Question

What is the value of the acceleration on the surface of a planet that has twice the mass of earth and twice its radius?

Answer 1

Explanations & Calculations

• Acceleration on the surface is the acceleration at the radial distance from the earth's centre.

$\qquad\qquad \begin{aligned} \small g&=\small G\frac{M_e}{r_e^2}\cdots(1)\\ \\ \text{Now}\\\small M&=\small 2M_e\\ \small r&=\small 2r_e\\ \\ \small\text{In (1)}\\ \small g_{new}&=\small G\frac{2M_e}{(2r_e)^2}\\ &=\small \frac{1}{2}\Big(G\frac{M_e}{r_e}\Big)\\ &=\small \frac{g}{2} \end{aligned}$

• New acceleration is a half that of the earth.