Question

2. FN) A Fig. 5.6 12 24 x(m) A body is under the action of a force F such that the force-displacement graph of the body is semicircle as shown above. The work done on the body by the force in moving through 24 meters is A. 36J B. 721 JC. 1441 J D. 28871 J
JAMB 1991 Ans: 7211 J or 226.3J 2 Aan 1201​

Answer 1

Statement:

A body is under the action of a force F such that the force-displacement graph of the body is semicircle as shown above. The work done on the body by the force in moving through 24 meters.

To find out:

The work done by the body.

Solution:

• Here force is F and let us consider the displacement as s.
• We know, work done = Fs.
• Here the area under the curve is Fs, i.e., work done.
• We know, area of a semicircle = $\frac{\pi \: {r}^{2} }{2}$where r is the radius.
• Here, radius (r) = 24 m
• Therefore, work done

$= \frac{\pi \: {r}^{2} }{2} \\= \frac{(24) ^{2}\pi }{2} {m}^{2} \\ = \frac{576\pi}{2} {m}^{2} \\ = 288\pi \: {m}^{2}$

Answer:

The work done is 288π m².

Hope you could understand.

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