Question

A tray of mass $M=10kg$ is supported on two identical springs, each of spring constant k, as shown in the figure. When the tray is depressed a little and released, it executes simple harmonic motion of period 1.5 s. When a block of mass m is placed on the tray, the period of oscillation becomes 3.0 s. The value of m is

• A. 10 kg
• B. 20 kg
• C. 30 kg
• D. 40 kg

Answer 1

The correct option is C

30 kg

Here, equivalent spring constant, $k^{\prime }=k+k=2k$
$\therefore T_1=2\pi \sqrt{\frac{M}{2k}}$ .....(1)
and $T_2=2\pi \sqrt{\frac{M+m}{2k}}$ .....(2)
From equations (1) and (2), $\frac{T_2}{T_1}=\sqrt{\frac{M+m}{M}}$
$\Rightarrow \frac{3.0}{1.5}=\sqrt{\frac{10+m}{10}}$
$\Rightarrow m=30kg$
Hence, the correct choice is (c).