Q127 / 160 · AP EAMCET 2023 (19 May Shift 1) · Physics
A toy of mass $20 \mathrm{~g}$ at rest acquires a velocity $(3 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}) \mathrm{ms}^{-1}$ in 2 seconds. Then the power of the toy is
- A$0.975 \mathrm{~W}$
- B$0.325 \mathrm{~W}$
- Correct answerC$1.3 \mathrm{~W}$
- D$0.065 \mathrm{~W}$
Solution
Mass of toy, $\mathrm{m}=20 \mathrm{~g}=0.02 \mathrm{~kg}$
Velocity, $\overrightarrow{\mathrm{v}}=(3 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}) \mathrm{m} / \mathrm{s}$
$$
|\overrightarrow{\mathrm{v}}|=\sqrt{9+4}=\sqrt{13} \mathrm{~m} / \mathrm{s}
$$
Power of the toy is defined by
$$
\begin{aligned}
& P=F v \\
& =\frac{\mathrm{mv}^2}{t} \\
& =\frac{0.02 \times 13}{2}=0.13 \mathrm{~W}
\end{aligned}
$$
Hence, the correct answer is option: 'C'.