A solid circular disc of mass 50 kg rolls along a horizontal floor so that its center of mass has a speed of 0.4 m/s. The absolute value of work done on the disc to stop it is ______ J.

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Solution

Q.
A solid circular disc of mass 50 kg rolls along a horizontal floor so that its center of mass has a speed of 0.4 m/s. The absolute value of work done on the disc to stop it is ______ J. [2024]

Ans.
(6) Using work energy theorem

$W = Δ K E = 0 - (\frac{1}{2} m v^{2} + \frac{1}{2} I ω^{2})$

$W = 0 - \frac{1}{2} m v^{2} (1 + \frac{K^{2}}{R^{2}})$

$= - \frac{1}{2} \times 50 \times {0.4}^{2} (1 + \frac{1}{2}) = - 6 J$

$Absolute work = + 6 J$

$W = - 6 J$ $| W | = 6 J$

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