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? [2019]

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Solution

Q.
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 [2019]

1 1 J

2 3 J

3 30 kJ

4 2 J

Ans.
(2)

Required work done $= - (K_{f} - K_{i}) = 0 + K_{i} = K_{i}$

$= \frac{1}{2} I ω^{2} + \frac{1}{2} m v^{2} = \frac{1}{2} (\frac{1}{2} m R^{2}) \frac{v^{2}}{R^{2}} + \frac{1}{2} m v^{2}$

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

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