HSC Board

A simple pendulum of length 100 cm performs S.H.M. Find the restoring force acting on its bob of mass 50 g when the displacement from the mean position is 3 cm.

The data that we can put forward from this question is ,

Length L= 100cm = 1m

Mass m = 50g = 0.050kg

Displacement x = 3cm = 0.03m

To find , Restoring Force F = ?

Restoring force F is,

$https://latex.codecogs.com/svg.image?F = mg sin \theta$

As θ is small, sinθ = θ

F = mgθ

$https://latex.codecogs.com/svg.image?F = mg\frac{x}{L}$

F = 0.05 x 9.8 x 0.03

F = 0.0147 N

$https://latex.codecogs.com/svg.image?F = 1.47x10^{-2}N$

The mass of the earth is 6 x 10²⁴ kg. The distance between the earth and the Sun is 1.5x 10¹¹ m. If the gravitational force between the two is 3.5 x 10²² N, what is the mass of the Sun?