Question

The free-fall acceleration at the surface of planet 1 is 16 m/s2. The radius and the mass of planet 2 are twice those of planet 1.
What is g on planet 2?

Answer 1

Answer:

$8m/s^2$

Explanation:

We are given that

Acceleration at the surface of planet 1=$16m/s^2$

We have to find the g on planet 2.

Let R be the radius of planet 1 and M be mass of planet 1.

According to question

Mass of planet 2=2M

Radius of planet 2=2R

Acceleration due to gravity on the planet is given by

$g=\frac{GM}{R^2}$

Using the formula

$16=\frac{GM}{R^2}$..(1)

$g=\frac{2GM}{(2R)^2}=\frac{GM}{2R^2}$...(2)

Divide Equation(2)  by equation (1)

$\frac{g}{16}=\frac{1}{2}$

$g=\frac{1}{2}\times 16=8m/s^2$

Hence,g on planet 2=$8m/s^2$