Q126 / 160 · TS EAMCET 2024 (10 May Shift 2) · Physics

The kinetic energy of a body of mass 4 kg moving with a velocity of $(2 \hat{i}-4 \hat{j}-\hat{k}) \mathrm{ms}^{-1}$ is

  • A
    84 J
  • B
    63 J
  • Correct answer
    C
    42 J
  • D
    21 J

Solution

$\begin{aligned} & \mathrm{m}=4 \mathrm{~kg}, \overrightarrow{\mathrm{v}}=(2 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}-\hat{\mathrm{k}}) \mathrm{ms}^{-1} \\ \therefore & \mathrm{v}=|2 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}-\hat{\mathbb{k}}|=\sqrt{(2)^2+(-4)^2+(-1)^2}=\sqrt{21} \\ \therefore & \mathrm{~K} \cdot \mathrm{E}_0=\frac{1}{2} \mathrm{mv}^2=\frac{1}{2} \times 4 \times 21=42 \mathrm{~J}\end{aligned}$

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

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