Two persons A and B perform same amount of work in moving a body… | JEE Main 2021 (27 Aug, Shift 1)

Q14JEE Main 2021 · 27 AUG · SHIFT 1Easy

Work by a Constant Force

Two persons A and B perform same amount of work in moving a body through a certain distance d with application of forces acting at angle 45 ${}^\circ$ and 60 ${}^\circ$ with the direction of displacement respectively. The ratio of force applied by person A to the force applied by person B is $\frac{1}{\sqrt{x}}$ . The value of x is .....................

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Answer: 2

Same work over the same $d$ : $F_A d\cos 45^\circ = F_B d\cos 60^\circ$
$\frac{F_A}{F_B} = \frac{\cos 60^\circ}{\cos 45^\circ} = \frac{1/2}{1/\sqrt{2}} = \frac{1}{\sqrt{2}}$
Comparing with $\frac{1}{\sqrt{x}}$ , $x = 2$ .

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