Class 11th Physics Work, Energy and Power

Figure shown two blocks A and B having mass 2kg and 4kg moving with a speed 4 m/sec and 2 m/sec respectively. The maximum compression in the spring and final velocity of 2kg block and respectively.

Option 1 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mroot> <mrow> <mfrac> <mrow> <mn>2</mn> <mn>4</mn> </mrow> <mrow> <mn>4</mn> <mn>5</mn> </mrow> </mfrac> <mi>m</mi> <mo>,</mo> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span>3 m/s</p>

Option 2 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mroot> <mrow> <mfrac> <mrow> <mn>2</mn> <mn>4</mn> </mrow> <mrow> <mn>2</mn> <mn>5</mn> </mrow> </mfrac> <mi>m</mi> <mo>,</mo> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span>3 m/s</p>

Option 3 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mroot> <mrow> <mfrac> <mrow> <mn>2</mn> <mn>4</mn> </mrow> <mrow> <mn>4</mn> <mn>5</mn> </mrow> </mfrac> <mi>m</mi> <mo>,</mo> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span>4/3 m/s</p>

Option 4 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mroot> <mrow> <mfrac> <mrow> <mn>2</mn> <mn>4</mn> </mrow> <mrow> <mn>2</mn> <mn>5</mn> </mrow> </mfrac> <mi>m</mi> <mo>,</mo> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span>8/3 m/s</p>

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Alok Kumar Singh | Contributor-Level 10

5 months ago

Correct Option - 3

Detailed Solution:

$\frac{1}{2} μ v_{r}^{2} = \frac{1}{2} k x^{2}$

$x = {V_{r e r}}^{2} \sqrt[]{\frac{μ}{k}}$

$= 2 * \sqrt[]{\frac{8 / 6}{10}} = \sqrt[]{\frac{8}{15}}$

From conservation of momentum

2 * 4 + 4 * 2 = 2v₁ + 4v₂

8 = v₁ + 2v₂ ….(1)

From conservation of energy

$\frac{1}{2} * 2 * 4^{2} + \frac{1}{2} * 4 * 2^{2} = \frac{1}{2} * 2 * v_{1}^{2} + \frac{1}{2} * 4 * v_{2}^{2}$ …..(ii)

On solving $v_{1} = \frac{4}{3} m / s, v_{2} = \frac{10}{3} m / s$

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Physics Work, Energy and Power 2021

Physics Work, Energy and Power 2021

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