A ball of mass 100g is under a force which causes a displacement S in metres, given by the relation S=t3+t2 where t is in seconds. Work done by the force in 3 seconds
A
72.45J
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B
36.55J
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C
20J
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D
54.45J
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Solution
The correct option is D54.45J Given displacement of the ball, S=(t3+t2)m........(1) ⇒dS=(3t2+2t)dt
Acceleration a=d2Sdt2=6t+2 ∴ Force acting on ball at time t, F(t)=ma=0.1(6t+2)
Work done by force at time t is given by dW=F(t)dS=0.1(6t+2)(3t2+2t)dt =0.1(18t3+18t2+4t)dt
Therefore, total work done by force in 3 seconds W=∫dW=∫300.1(18t3+18t2+4t)dt =0.1[92t4+6t3+2t2]30 =0.1[7292+162+18] =0.1×10892=54.45J