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 $3$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

$T_1=2\pi \sqrt{\frac{M}{2K}}$

$T_2=2\pi \sqrt{\frac{M+m}{2K}}$

$⟹\frac{T_1}{T_2}=\frac{\sqrt{M}}{\sqrt{M+m}}$

$⟹\frac{1.5}{3}=\sqrt{\frac{10}{10+m}}$

$⟹\frac{1}{4}=\frac{10}{m+10}$

$⟹m=30kg.$