Question

A rod of mass $\pi$ kg and length $1$ m rests on a smooth horizontal ground and is hinged at one of its end. At the other end, a horizontal force $F$, of magnitude $3$ N, is applied whose magnitude is constant and the direction is always perpendicular to the rod. When the rod rotates by $\frac{\pi }{2}$ rad angle, power supplied by this force at that instant is :

• A. zero
• B. $50$ Watt
• C. $\frac{90}{\pi }$ watt
• D. $9$ watt

Answer 1

The correct option is D $9$ watt

$W_F=KE\to where{W}_F=\iota \theta =\left(Fl\right)\left(\frac{\pi }{2}\right)$
$\left(Fl\right)\frac{\pi }{2}=\frac{1}{2}\left(\frac{m{l}^2}{3}\right){\omega }^2$
$\omega =\sqrt{\frac{3F\pi }{ml}}$
$P_F=\left(\iota \right)\left(\omega \right)$
$P_F=\left(Fl\right)\sqrt{\frac{3F\pi }{ml}}$
$P_F=\sqrt{\frac{3F^3\pi l}{m}}=\sqrt{\frac{3\times (3{)}^3\times \pi \times 1}{\pi }}=9watt$