Question

A mass 'm' is attached to a spring oscillate with a period of 2 seconds. If the mass is increased by 3 kg, the period increased by 1 second. Find the initial mass ‘m’ assuming Hook’s law is obeyed?

• A. 2.4 kg
• B. 5.6 kg
• C. 1 kg
• D. 3.4 kg

Answer 1

The correct option is A 2.4 kg

$2=2\pi \sqrt{\frac{m}{K}}.....\left(1\right)$
Also $3=2\pi \sqrt{\frac{m+3}{K}}.....\left(2\right)$
Squaring (1) and (2) and dividing $\frac{4}{9}=\frac{mK}{K(m+3)}$
9m = 4m + 12;
5m = 12;
$m=\frac{12}{5}=2.4kg$