Question

A disc of radius 2 m and mass 100 kg rolls on a horizontal floor. Its centre of mass has speed of 20 cm/s. How much work is needed to stop it ?
(1) 3 J
(2) 30 kJ
(3) 2 J
(4) 1 J

Answer 1

3J of work is needed to stop it.

Step by step explanation:

From the given,

Radius of disc = 2 m.

Weight of rolls = 100 kg

Speed =  20 cm/s= $20\times 10^{-2}$

The change in kinetic energy is equal to work required.

$Initial\, kinetic\,energy=\frac{1}{2}mv^{2}+\frac{1}{2}I\omega ^{2}= \frac{3}{4}mv^{2}$........(1)

Final kinetic energy = 0

Substitute the given values in equation (1)

      $=\frac{3}{4}\times 100\times (20\times 10^{-2})^{2}=3J$

Therefore, 3J of work is needed to stop it.