A body of mass m is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of 2 s. When the mass m is increased by 1 kg, the time period of oscillations becomes 4 s. The value of m (in kg) is

# A body of mass m is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of 2 s. When the mass m is increased by 1 kg, the time period of oscillations becomes 4 s. The value of m (in kg) is

1. A

$\frac{3}{4}$

2. B

$\frac{4}{3}$

3. C

$\frac{3}{2}$

4. D

$\frac{1}{3}$

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### Solution:

Time period,

$\mathrm{T}=2\mathrm{\pi }\sqrt{\frac{\mathrm{m}}{\mathrm{k}}}$

Case I              ${\mathrm{T}}_{1}=2\mathrm{\pi }\sqrt{\frac{\mathrm{m}}{\mathrm{k}}}$                                           …(i)

Case II When the mass m increased by 1 kg, then net mass = m + 1

…(ii)

On dividing Eq. (ii) by Eq. (i), we get

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