Q123 / 180 · KCET 2025 · Physics

A body of mass 0.25 kg travels along a straight line from $\mathrm{x}=0$ to $\mathrm{x}=2 \mathrm{~m}$ with a speed $\mathrm{v}=\mathrm{k} \mathrm{x}^{3 / 2}$ where k $=2$ SI units. The work done by the net during this displacement is

  • A
    8 J
  • B
    16 J
  • C
    32 J
  • Correct answer
    D
    4 J

Solution

$\begin{aligned} & \mathrm{W}_{\text {net }}=\Delta \mathrm{KE} \\ & =\frac{1}{2} \mathrm{mv}^2-\frac{1}{2} \mathrm{mu}^2 \\ & =\frac{1}{2} \times 0.25\left(\mathrm{k}(2)^{3 / 2}\right)^2-0 \\ & =\frac{1}{2} \times 0.25 \times 2^2 \times 2^3 \\ & =4 \mathrm{~J}\end{aligned}$

Hence, the correct answer is option: 'D'.

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