Question

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

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

Answer 1

Answer: (C)

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