Q127 / 160 · AP EAMCET 2022 (05 Jul Shift 2) · Physics

A force $\overrightarrow{\mathrm{F}}=4 \hat{\mathrm{i}}-15 \hat{\mathrm{j}} \mathrm{N}$, acts on a body resulting in a displacement of $6 \hat{i}$. If the body had a kinetic energy of 7 joules at the beginning of the displacement, the kinetic energy at the end of the displacement is

  • A
    $24 \mathrm{~J}$
  • Correct answer
    B
    $31 \mathrm{~J}$
  • C
    $30 \mathrm{~J}$
  • D
    $25 \mathrm{~J}$

Solution

Work done $=\overrightarrow{\mathrm{F}} \cdot \overrightarrow{\mathrm{S}}$ $\begin{aligned} & \Rightarrow \quad \Delta \mathrm{K}=\overrightarrow{\mathrm{F}} \cdot \overrightarrow{\mathrm{S}} \\ & \Rightarrow \quad \mathrm{K}_{\mathrm{f}}-7=(4 \hat{\mathrm{i}}-15 \hat{\mathrm{j}}) \cdot(6 \hat{\mathrm{i}}) \Rightarrow \mathrm{K}_{\mathrm{f}}-7=24 \Rightarrow \mathrm{K}_{\mathrm{f}}=31 \mathrm{~J}\end{aligned}$

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

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