Question

A $50\text{kg}$ girl is swinging on a swing. Then, the power delivered while moving with a velocity of $2\text{m/s}$ upwards and the rope makes an angle of ${60}^{\circ }$ with the vertical is

$($Assume girl starts from rest and $g=9.8{\text{m/s}}^2)$

• 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 $490\sqrt{3}\text{W}$

From the diagram, we can clearly see that there are two forces acting on girl, tension and weight.


Power developed by the tension $T$ will be zero because $\overrightarrow{T}\perp \overrightarrow{v}$.

Now, power due to weight will be,

$P_w=\overrightarrow{W}\cdot \overrightarrow{v}$

$\Rightarrow P_w=mgv\cos ({90}^{\circ }+\theta )=mgv\cos ({90}^{\circ }+{60}^{\circ })$

$\Rightarrow P_w=-mgv\sin {60}^{\circ }=-50\times 9.8\times 2\times \frac{\sqrt{3}}{2}$

$\therefore P_{net}=P_w=-490\sqrt{3}\text{W}$

So, the net power delivered is $490\sqrt{3}\text{W}$.

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