Question

Calculate the value of g on an imaginary planet of mass 1 x 10²⁴ kg and of radius 2 x 10⁶ m. Take G = 6.7 x 10^-11 Nm² kg^-2.

Answer 1

Given:

The mass of the planet (M) = 1 x 10²⁴ kg.

The radius of the planet (R) = 2 x 10⁶ m.

Universal gravitational constant (G) = 6.7 x 10^-11 Nm² kg^-2.

Required to find:

The value of g on the planet.

Solution:

The magnitude of the acceleration (g) produced in a body that is falling freely on the surface of a planet is given by $g=\frac{GM}{R^2}$.

By substituting the given values in the above equation, we get

$g=\frac{GM}{R^2}=\frac{(6.7x{10}^{-11})x(1x{10}^{24})}{{(2x{10}^6)}^2}=\frac{6.7x{10}^{13}}{4x{10}^{12}}=16.7m{s}^{-2}$

Therefore, the value of ‘g’ on the given planet is 16.7 ms^-2.