Question

# 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 statements is/are true?

A

In equilibrium, the spring will be stretched by 1 cm

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B

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

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C

The frequency of oscillation will be nearly 5 Hz.

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D

If the system is taken to the moon, the frequency of oscillation will be the same as on the earth.

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Solution

## The correct options are A In equilibrium, the spring will be stretched by 1 cm B If the mass is raised till the spring is un-stretched state and them released, it will go down by 2 cm before moving upwards. C The frequency of oscillation will be nearly 5 Hz. D If the system is taken to the moon, the frequency of oscillation will be the same as on the earth. Let's say that the spring stretches to a distance x0 we have kx0=mg ⇒ 200× x0=0.2×10 x0=1100m=1 cm the new mean position is 1 cm below the natural length of the spring. If it is released from its natural length, it would be 1 cm above it's mean position. When released it would go 1 cm to the other side i.e., a total of 2 cm from the natural length. Frequency is independent of acceleration due to gravity. Hence all the four options are correct.

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