First slide

Torque

Question

A one kg stone attached to the end of a 60 cm chain is revolving at the rate of 3 revolutions/second. If after 30 second, it is making only one revolution per second, find the mean torque

Moderate

A

0.45 N m
B

0.35Nm
C

0.25Nm
D

0.15Nm

Solution

The torque $τ$ is given by
$τ = \frac{change in momentum}{time taken}$
Here, $L_{1} = {mr}^{2} ω_{1} = {mr}^{2} \times (2 {πv}_{1})$
and $L_{2} = {mr}^{2} ω_{2} = {mr}^{2} \times (2 {πv}_{2})$
so, change in momentum
$\begin{array}{l} = {mr}^{2} \times 2 π (v_{1} - v_{2}) \\ ∴ τ = \frac{{mr}^{2} \times 2 π (v_{1} - v_{2})}{t} \\ = \frac{1 (0 \cdot 6)^{2} \times 2 π (3 - 1)}{30} \\ = 0 \cdot 15 N - m . \end{array}$

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