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Q.

A block of mass m = 1 kg falls from a height h = 0.4 m on a massless spring of stiffness constant $k = 300 N m^{- 1} . I f g = 10 m / s^{2},$ then

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a

When compression in the spring is $\frac{1}{30} m,$ the acceleration of the block is zero

b

Maximum acceleration of the block is $50 m / s^{2}$

c

Maximum compression in the spring is 0.2 m

d

Maximum extension in the spring is 0.2 m

answer is A, B, C.

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Detailed Solution

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Acceleration will be zero when $k x_{1} = m g$
$300 \times x_{1} = 1 \times 10 \Rightarrow x_{1} = \frac{1}{30} m$
For maximum compression x $m g (0.4 + x) - \frac{1}{2} k x^{2} = 0$
$10 (0.4 + x) - 150 x^{2} = 0 \Rightarrow x = 0.2 m$
For maximum acceleration $= \frac{300 (0.2) - 10 \times 1}{1} = 50 {m/s}^{2}$

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