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
• B. If the mass is raised till the spring is in 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.

Answer 1

Answer: (A), (B), (C), (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 $x_{0}wehavek{x}_0=mg$

$\Rightarrow 200\times x_0=0.2\times 10$

$x_0=\frac{1}{100}m=1cm$

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.