A mass m attached to a spring oscillates every 2 sec. If the mass is increased by 2 kg, then time-period increases by 1 sec. The initial mass is

The correct option is C. 1.6 kg

The time period of the oscillation of a spring-mass system is given by,

$T=2\pi \sqrt{\frac{m}{k}}$

where m = mass and k = spring constant.

For the same 'k' value, we have,

$T\propto \sqrt{m}$

$\Rightarrow \frac{T_2}{T_1}=\sqrt{\frac{m_2}{m_1}}$

$\Rightarrow \frac{3}{2}=\sqrt{\frac{m+2}{m}}$

$\Rightarrow \frac{9}{4}=\frac{m+2}{m}$

$\Rightarrow 9m=4m+8$
$\Rightarrow m=\frac{8}{5}kg=1.6kg$.

Thus the initial mass is 1.6 kg.