Question

A block of mass $M$ attached to an ideal spring oscillates with a time period of $2$ seconds. If an additional mass $2kg$ is attached to this block then time period of oscillation increases by $1$ sec. The value of $M$ is

• A. $1.2kg$
• B. $1.6kg$
• C. $2kg$
• D. $2.4kg$

Answer 1

Answer: (B)

$1.6kg$

$T_1=2sec$
$T_2=3sec$
$T=2\pi \sqrt{\frac{m}{k}}$
$T\alpha \sqrt{m}$
$\frac{T_1}{\sqrt{m_1}}=\frac{T_2}{\sqrt{m_2}}$
$\frac{2}{\sqrt{M}}=\frac{3}{\sqrt{M+2}}$
$4M+8=9M$
$m=\frac{8}{5}$
$m=1.6kg$