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

Answer 1

The correct option is C $30kg$

From Formula of time period, we get equations 1 and 2.
$1.5=2\pi \sqrt{\frac{10}{k_{eq}}}...\left(1\right)$
$3=2\pi \sqrt{\frac{10+m}{k_{eq}}}...\left(2\right)$
Dividing 2 by 1, we get,
$m=30kg.$
Hence, option C is correct.