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 -

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

Option 2 -

$\sqrt[v]{\frac{2 m}{9 k}}$

Option 3 -

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

Option 4 -

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

2 Views | Posted 4 weeks ago

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

4 weeks 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

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

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

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

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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

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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

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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