Question

A tray of mass M = 10 kg is supported on two identical springs, each of spring constant k. as shown in 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 $T_1=2\pi \sqrt{\frac{M}{2k}}$
$And{T}_2=2\pi \sqrt{\frac{M+m}{2k}}$
$\therefore \frac{T_2}{T_1}=\sqrt{\frac{M+m}{M}}$
$Or,\frac{3.0}{1.5}=\sqrt{\frac{10+m}{10}}$