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Q.

A horizontal plank has a rectangular block placed on it. The plank starts oscillating vertically and simple harmonically with an amplitude of 40cm. The block just looses contact with this plank when the latter is at momentary rest, then

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a

The period of oscillation is $\frac{2 π}{5} s$

b

The block weighs double its weight when the plank is at one the positions of momentary rest

c

The block weighs double its weight when the plank half way down

d

The period of oscillation is $\frac{π}{5} s$

answer is A, B.

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Detailed Solution

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As the block loses contact with the plank, when it is at the highest position,
$m g - N = m ω^{2} A$ $(∵ N = 0)$
$ω^{2} = \frac{g}{A} \Rightarrow T = \frac{2 π}{ω} = 2 π \sqrt{\frac{A}{g}} \Rightarrow T = \frac{2 π}{5} s$
At lower extreme, acceleration is g(upwards) $N - m g = m a \Rightarrow N = 2 m g$

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