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An object of mass 500 g, initially at rest, is acted upon by a variable force whose X-component varies with X in the manner shown. The velocities of the object at the points X = 8 m and X = 12 m, would have the respective values of (nearly)

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18 m/s and 20.6 m/s

18 m/s and 24.4 m/s

23 m/s and 20.6 m/s

23 m/s and 24.4 m/s

answer is D.

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Detailed Solution

From work-energy theorem

$ΔK = work = area under F - x graph ,$

$From x = 0 to x = 8 m, \frac{1}{2} {mv}^{2} = 100 + 30$

$\Rightarrow v^{2} = 520 \Rightarrow v = \sqrt{520} ≃ 23 m / s$

$From x = 0 to x = 12 m, \frac{1}{2} {mv}^{2} = 100 + 30 - 47.5 + 20$

$\Rightarrow v = \sqrt{410} \Rightarrow v ≃ 20.6 m / s Hence appropriate option is 23 m / s and 20.6 m / s$

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