A spring-block system, shown in figure, is oscillating on a frictionless horizontal surface with amplitude 4 cm and maximum velocity of the block is 8 m/s. When the block is at its extreme position, another identical block is gently placed over it and the two blocks start oscillating together without any relative motion between them. Then time period of oscillation of this composite block is

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$\frac{π}{75} s$

$\frac{π}{50 \sqrt{2}} s$

$\frac{π}{25 \sqrt{2}} s$

$\frac{2 π}{25} s$

answer is C.

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Detailed Solution

Initially, $ω = \sqrt{\frac{k}{m}} and V_{\max} = ω A = A \sqrt{\frac{k}{m}}$
After the block is placed, $ω' = \sqrt{\frac{k}{2 m}} = \frac{ω}{\sqrt{2}}$
New time period of oscillation $T' = \frac{2 π}{ω'} = \frac{2 π}{ω / \sqrt{2}} = \sqrt{2} (\frac{2 π}{ω})$