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 45º and 60º with the direction of displacement respectively. The ratio of force applied by person A to the force applied by person B is 1x. The value of x is ....... .

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answer is 2.

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Detailed Solution

Given, work done by both person is same,

           WA=WB

Direction of first force with displacement, θ1 = 45°

Direction of second force with displacement, θ2 = 60°

Ratio of force applied by person A to force applied by person B is FA : FB=1 : x.

Work done by both person is same,

WA=WBFAdcosθ1=FBdcosθ2

( distance is same for both = d)

         FAFB=cosθ1cosθ2=cos60cos45    FAFB=1212=12FAFB=1x=12x=2

Thus, the value of x is 2.

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