Q95 / 180 · NEET 2025 · Physics
A ball of mass 0.5 kg is dropped from a height of 40 m . The ball hits the ground and rises to a height of 10 m . The impulse imparted to the ball during its collision with the ground is (Take $\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^2$ )
- Correct answerA21 NS
- B7 NS
- C0
- D84 NS
Solution
$\begin{aligned}
v_i & =-\sqrt{2 \mathrm{gh}_i}=-\sqrt{2 \times 9.8 \times 10}=-28 \mathrm{~m} / \mathrm{s} \\
\mathrm{v}_{\mathrm{f}} & =\sqrt{2 \mathrm{gh}_{\mathrm{i}}}=\sqrt{2 \times 9.8 \times 10}=14 \mathrm{~m} / \mathrm{s} \\
\overrightarrow{\mathrm{I}} & =\Delta \overrightarrow{\mathrm{P}}=\mathrm{m} \overrightarrow{\mathrm{v}}_{\mathrm{f}}-\mathrm{m} \overrightarrow{\mathrm{v}}_{\mathrm{i}} \\
& =\mathrm{m}\left[\overrightarrow{\mathrm{v}}_{\mathrm{f}}-\overrightarrow{\mathrm{v}}_{\mathrm{i}}\right]=0.5[14-(-28)] \\
& =0.5 \times 42=21 \mathrm{NS}
\end{aligned}$
Hence, the correct answer is option: 'A'.