Question

A $50\text{kg}$ girl is swinging on a swing starting from rest. The magnitude of power delivered, when the rope (of negligible mass) is making an angle of ${60}^{\circ }$ with the downward vertical velocity of $2\text{m/s}$, directed upwards is,

• A. $980\text{W}$
• B. $490\text{W}$
• C. $490\sqrt{3}\text{W}$
• D. $245\text{W}$

Answer 1

The correct option is C $490\sqrt{3}\text{W}$

Two forces are acting on the bob namely, tension and weight.
Power will be delivered by tangential forces only. So, power of tension will be zero as it is radial in direction.
Now, $P=F_t\times v$


$\therefore P=mgv\cos ({90}^{\circ }+{60}^{\circ })=-mgv\sin {60}^{\circ }$
$=-50\times 9.8\times \times 2\times \frac{\sqrt{3}}{2}=-490\sqrt{3}\text{W}$
Therefore, $|P|=490\sqrt{3}\text{W}$

Hence, $\left(C\right)$ is the correct answer.