Looking for classes? Ksquare Career Institute, Bengaluru →
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 3s. When the mass m is increased by 1 kg, the time period of oscillations becomes 5 s. The value of m in kg is:
A
$\frac{16}{9}$
B
$\frac{9}{16}$
C
$\frac{3}{4}$
D
$\frac{4}{3}$
Explanation
$T^2 \propto m$.
Detailed Solution
$T = 2\pi\sqrt{\frac{m}{k}}$
$3 = 2\pi\sqrt{\frac{m}{k}}$ ...(1), $5 = 2\pi\sqrt{\frac{m + 1}{k}}$ ...(2)
$\frac{(1)^2}{(2)^2}$: $\frac{9}{25} = \frac{m}{m + 1} \Rightarrow m = \frac{9}{16}$
$3 = 2\pi\sqrt{\frac{m}{k}}$ ...(1), $5 = 2\pi\sqrt{\frac{m + 1}{k}}$ ...(2)
$\frac{(1)^2}{(2)^2}$: $\frac{9}{25} = \frac{m}{m + 1} \Rightarrow m = \frac{9}{16}$