Class 11th Physics System of Particles and Rotational Motion Physics

A block of mass $2 m$ is moving with speed $v$ towards a spring block system as shown in the figure. if collision of the two blocks is perfectly inelastic then maximum compression in the spring will be

Option 1 - <p><span class="mathml" contenteditable="false"> <math> <mroot> <mrow> <mrow> <mfrac> <mrow> <mrow> <mn>3</mn> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <mi>k</mi> </mrow> </mrow> </mfrac> </mrow> </mrow> <mrow> <mi>v</mi> </mrow> </mroot> </math> </span></p>

Option 2 - <p><span class="mathml" contenteditable="false"> <math> <mroot> <mrow> <mrow> <mfrac> <mrow> <mrow> <mn>2</mn> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <mn>9</mn> <mi>k</mi> </mrow> </mrow> </mfrac> </mrow> </mrow> <mrow> <mi>v</mi> </mrow> </mroot> </math> </span></p>

Option 3 - <p><span class="mathml" contenteditable="false"> <math> <mroot> <mrow> <mrow> <mfrac> <mrow> <mrow> <mn>2</mn> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> <mi>k</mi> </mrow> </mrow> </mfrac> </mrow> </mrow> <mrow> <mi>v</mi> </mrow> </mroot> </math> </span></p>

Option 4 - <p><span class="mathml" contenteditable="false"> <math> <mroot> <mrow> <mrow> <mfrac> <mrow> <mrow> <mn>4</mn> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> <mi>k</mi> </mrow> </mrow> </mfrac> </mrow> </mrow> <mrow> <mi>v</mi> </mrow> </mroot> </math> </span></p>

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Answered by

Alok Kumar Singh | Contributor-Level 10

4 months ago

Correct Option - 4

Detailed Solution:

Applying conservation of momentum for collision of blocks

$2 m v + 0 = 3 m v^{'}$

$? v^{'} = \frac{2 v}{3} \dots (1)$

Now, from conservation of energy

$\frac{1}{2} * 3 m * {v^{'}}^{2} = \frac{1}{2} k x_{0}^{2}$

$x_{0} = \sqrt[]{\frac{3 m v^{' 2}}{k}} = v' \sqrt[]{\frac{3 m}{k}}$

$= \frac{2 v}{3} \sqrt[]{\frac{3 m}{k}} = v \sqrt[]{\frac{4 m}{3 k}}$

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Physics System of Particles and Rotational Motion 2025

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