Question

The mass m attached to a spring oscillates with a period of 2s. If mass is increased by 2 kg, the period increase by 1s. Find the initial mass M assuming that Hooke’s law is obeyed

• A. 1 kg
• B. 1.5 kg
• C. 1.9 kg
• D. 1.6 kg

Answer 1

The correct option is D

1.6 kg

$T\propto \sqrt{m.}\text{since T}=2\pi \sqrt{\frac{m}{k}}2\propto \sqrt{m}3\propto \sqrt{m+2}\Rightarrow \frac{m+2}{m}=\frac{9}{4}\Rightarrow 4m+8=9mm=\frac{8}{5}=1.6kg$