Question

A girl of mass $50kg$ swinging on a cradle. If she moves with a velocity of $2m{s}^{-1}$ upwards in a direction making an angle $60^{\circ }$ with the vertical, then the power generated is $\left(g=9.8m{s}^{-2}\right)$

• A. $245W$
• B. $490\sqrt{2}W$
• C. $490\sqrt{3}W$
• D. $980W$

Answer 1

Answer: (C)

Given,
Mass of the girl $(m)=50kg$
Velocity $(v)=2m/s$
Angle $(\theta )=60^{\circ }$
$g=9.8m/s^2$
Work needed to displace the girl through a small arc of length $dS$ is
$=mg\sin 60^{\circ }\times ds$
But $ds=vdt$
Now, work done in time $dt$
$=mg\sin 60^{\circ }vdt$
Power at that instant $=mg\sin 60^{\circ }\cdot V$
$=50\times 9.8\times \sin 60^{\circ }\times 2$
$=50\times 9.8\times \frac{\sqrt{3}}{2}\times 2$
$=25\times 9.8\times \sqrt{3}\times 2$
$=490\sqrt{3}W$