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 -

$\sqrt[]{\frac{24}{45} m,}$ 3 m/s

Option 2 -

$\sqrt[]{\frac{24}{25} m,}$ 3 m/s

Option 3 -

$\sqrt[]{\frac{24}{45} m,}$ 4/3 m/s

Option 4 -

$\sqrt[]{\frac{24}{25} m,}$ 8/3 m/s

3 Views | Posted 3 weeks ago

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

3 weeks ago

Correct Option - 3

Detailed Solution:

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

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

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

From conservation of momentum

2 × 4 + 4 × 2 = 2v₁ + 4v₂

8 = v₁ + 2v₂ ….(1)

From conservation of energy

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

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

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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.

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