Question

A sphere of radius $10cm$ and mass $25kg$ is attached to the lower end of steel wire of length $5m$ and diameter of $4mm$ which is suspended from the ceiling of a room. The point of support is $521cm$ above the floor. When the sphere is set swinging as a simple pendulum, its lowest point just grazes the floor. Calculate the velocity of the ball at its lowest position.

Answer 1

Using the formula of youngs modulus and then comparing it to the formula of the force we get,

$Y=\frac{\frac{F}{A}}{\frac{\Delta l}{l}}$

$\Rightarrow F=\frac{YA\Delta l}{l}=mg+\frac{m{v}^2}{l}$

$\Rightarrow v=\sqrt{\frac{l}{m}(\frac{YA\Delta l}{l}-mg)}$

$v=\sqrt{\frac{5}{25}(\frac{2\times {10}^{11}\times \pi \times 4\times {10}^{-6}\times {10}^{-2}}{5}-250)}$

$=\sqrt{\frac{1}{5}(\frac{8\pi }{5}\times {10}^3-250)}=30.9m/s$