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Question

An object is displaced from position vector r1=(2^i+3^j) m to r2=(4^i+6^j) m under a force F=(3x2^i+2y^j) N. Find the work done.

A
83 J
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B
38 J
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C
83 J
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D
38 J
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Solution

The correct option is A 83 J
Given, F=3x2^i+2y^j N
Initial position, (r1)=(2^i+3^j) m(2,3)(x1,y1)
Final position, (r2)=(4^i+6^j) m(4,6)(x2,y2)
Since, the given force is variable in x and y, displacement of object, ds=dx^i+dy^j

Then, work done W=F.ds=x2x1Fxdx+y2y1Fydy=423x2dx+632ydy=x3|42+y2|63=(4323)+(6232)=(648)+(369)=83 J

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