Q.

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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a

18 m/s and 20.6 m/s

b

18 m/s and 24.4 m/s

c

23 m/s and 24.4 m/s

d

23 m/s and 20.6 m/s

answer is D.

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Detailed Solution

From work-energy theoremΔK= work = area under F-x graph  From x = 0 to x = 8 m 12mv2=100+30 v2=520 v=520≃23 m/s From x = 0 to x = 12 m 12mv2=100+30-47.5+20 v=410 v≃20.6 m/s Hence appropriate option is 23 m/s and 20.6 m/s
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