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NEET 2006
Exam
NEET
Year
2006
Subject
Physics
Chapter
Work, Power and Energy

NEET 2006 · Physics · Work, Power and Energy

A body of mass 3 ~kg is under a constant force which causes a...

A body of mass 3 kg3 \mathrm{~kg} is under a constant force which causes a displacement ss in metres in it, given by the relation s=13t2s=\frac{1}{3} t^2, where tt is in seconds. Work done by the force in 2 seconds is:

Options

  1. A195 J\frac{19}{5} \mathrm{~J}
  2. B519 J\frac{5}{19} \mathrm{~J}
  3. C38 J\frac{3}{8} \mathrm{~J}
  4. D83 J\frac{8}{3} \mathrm{~J}

Correct answer

D. 83 J\frac{8}{3} \mathrm{~J}

Step-by-step solution

It is given that: s=t23s=\frac{t^2}{3} Differentiating w.r.t. tt we have U=dsdt=2t3U=\frac{d s}{d t}=\frac{2 t}{3} Again differentiating w.r.t. tt we have a=d2sdt2=23a=\frac{d^2 s}{d t^2}=\frac{2}{3} Now W=∫Fds=∫mads\mathrm{W}=\int \mathrm{F} d s=\int \mathrm{mads}=∫m×23×2t3dt=49m∫tdtW=49m×[t22]02=49×3×2=83 J\begin{aligned} & =\int m \times \frac{2}{3} \times \frac{2 t}{3} d t \\ & =\frac{4}{9} m \int t d t \\ W & =\frac{4}{9} m \times\left[\frac{t^2}{2}\right]_0^2 \\ & =\frac{4}{9} \times 3 \times 2=\frac{8}{3} \mathrm{~J} \end{aligned}$$
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