JEE Mains · Physics · STD 11 - Work,energy,power and collision
- JEE Mains 2020
- Hard
- MCQ
A particle of mass \(\mathrm{m}\) is dropped from a height \(h\) above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of \(\sqrt{2 \mathrm{gh}} .\) If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of \(\sqrt{\frac{\mathrm{h}}{\mathrm{g}}}\) is
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Answer & Solution
Correct Answer
(D) \(\sqrt{\frac{3}{2}}\)
Step-by-step Solution
Detailed explanation
Particles will collide after time \(\mathrm{t}_{0}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{gh}}}\)
at collision, \(\mathrm{v}_{\mathrm{A}}=\mathrm{gt}_{0} \quad \mathrm{v}_{\mathrm{B}}=\mathrm{u}_{\mathrm{B}}-\mathrm{gt}_{0}\)
\(\Rightarrow \mathrm{v}_{\mathrm{A}}=-\mathrm{v}_{\mathrm{B}}\)
at collision, \(\mathrm{v}_{\mathrm{A}}=\mathrm{gt}_{0} \quad \mathrm{v}_{\mathrm{B}}=\mathrm{u}_{\mathrm{B}}-\mathrm{gt}_{0}\)
\(\Rightarrow \mathrm{v}_{\mathrm{A}}=-\mathrm{v}_{\mathrm{B}}\)
Time taken by combined mass to reach the ground
time \(=\sqrt{\frac{2 \times 3 \mathrm{h} / 4}{\mathrm{g}}}=\sqrt{\frac{3 \mathrm{h}}{2 \mathrm{g}}}\)
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