Question

An astronaut drops a 3.6kg object onto the surface of a planet. It takes 2.6s to fall 1.86m to the ground. If the planet is known to have a redius of 8.4*10^6m. What is its mass?

Answer 1

here,

the mass of object , m = 3.6 kg

the tike taken , t = 2.6 s

let the acceleration due to gravity be g

h0 = u * t + 0.5 * g * t^2

1.86 = 0 + 0.5 * g * 2.6^2

solving for g

g = 0.5503 m/s^2

radius , R = 8.4 * 10^6 m

let the mass of planet be M

g = G * M /R^2

0.5503 = 6.67 * 10^-11 * M /( 8.4 * 10^6)^2

solving for M

M = 5.82 * 10^23 kg

the mass of planet is 5.82 * 10^23 kg