Q. A $60\ kg$ weight is dragged on a horizontal surface by a rope upto $2\ metres$. If coefficient of friction is $\mu = 0.5$, the angle of rope with the surface is $60{^\circ}$ and $g = 9.8m/s{ec}^{2}$, then work done is

A) $294\ joules$
B) $315\ joules$
C) $588\ joules$
D) $197\ joules$
Explanation

(b) Let body is dragged with force $P$, making an angle $60{^\circ}$ with the horizontal
$F_{k} =$ Kinetic friction in the motion$= \mu_{k}R$
From the figure $F_{k} = p\cos{60{^\circ}}$ and $R = mg - P\sin{60{^\circ}}$
$\therefore P\cos{60{^\circ}} = \mu_{k}(mg - P\sin{60{^\circ}})$
$\Rightarrow \frac{P}{2} = 0.5\left( 60 \times 10 - \frac{P\sqrt{3}}{2} \right)$
$\Rightarrow P = 315.1N$
$\therefore K_{k} = P\cos{60{^\circ}} = \frac{315.1}{2}N$
Work done $= F_{k} \times s = \frac{315.1}{2} \times 2 = 315\ Joule$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.

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