Question

A spring is made to oscillate after suspending a mass m from one of its ends. The time period obtained is 2 seconds. On increasing the mass by 2 kg, the period of oscillation is increased by 1 second. The initial mass m will be :

• A. 2 kg
• B. 1 kg
• C. 0.5 kg
• D. 1.6 kg

Answer 1

The correct option is D 1.6 kg

We know that ,

$T\propto 2\pi \sqrt{\frac{m}{k}}$ where $T$ is the time period , $m$ is the initial mass and $k$ is the spring constant .

Thus we can say ,

$T\propto \sqrt{m}$

$2s\propto \sqrt{m}$ -------- (i)

$2s+1s\propto \sqrt{m+2}$

Or $3s\propto \sqrt{m+2}$ -----------(ii)

Dividing (ii) by (i)

$\frac{3s}{2s}=K\frac{\sqrt{m+2}}{\sqrt{m}}$ \\ where K is a constant

Or,$\frac{(3{)}^2}{(2{)}^2}=\frac{m+2}{m}$ // squaring both sides

Or, $9m=4m+8$

Or, $5m=8$

Or, $m=1.6kg$