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Q.

A mass of 0.2 kg is attached to the lower end of a massless spring of force constant 200 N/m, the upper end of which is fixed to a rigid support. Which of the following statement is true?

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a

The frequency of the oscillation will be nearly 3 Hz.

b

In equilibrium, the spring will be stretched by 2 cm.

c

If the mass is raised till the spring becomes un-stretched and then released, it will go down by 2 cm before moving upwards.

d

The frequency of oscillation will be nearly 10 Hz.

answer is B.

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Detailed Solution

$At equilibrium, x = \frac{mg}{k} = \frac{0.2 \times 10}{200} = 0.01 m = 1 cm for maximum eleongation of the spring, mgx = \frac{1}{2} {kx}^{2} \Rightarrow x = 2 cm f = \frac{1}{2 π} \sqrt{\frac{k}{m}} = \frac{1}{2 π} \sqrt{\frac{200}{0.2}} \approx 5.0 Hz$

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