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A block of mass $4 k g$ moves on a horizontal smooth surface with velocity $31.4 m / s$ as shown in the figure. The block collides with spring of force constant $100 N / m$ and attached with a wall. The average value of the force of impact on the block due to the spring is

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$1600 N$

$1200 N$

$800 N$

$400 N$

answer is D.

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Detailed Solution

$f_{a v} = \frac{∆ P}{∆ t} = \frac{2 m v}{π \sqrt{\frac{m}{k}}} = \frac{4 (31.4 + 31.4)}{π \sqrt{\frac{4}{100}}} = \frac{2 \times 62.8}{3.14} \times 10 = 400 N$

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