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  4. 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° and 60° with the direction of displacement respectively. The ratio of force applied by person A to the force applied by person B is (1/√x) . The value of x is ldots ldots .

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Q. 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 $\ldots \ldots .$

JEE MainJEE Main 2021Work, Energy and Power

Solution:

Given $W _{ A }= W _{ B }$
$F _{ A } d \cos 45^{\circ}= F _{ B } d \cos 60^{\circ}$
$F _{ A } \times \frac{1}{\sqrt{2}}= F _{ B } \times \frac{1}{2}$
$\frac{ F _{ A }}{ F _{ B }}=\frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}}$
$X =2$