Question

In an experiment it was found that string vibrates in $n$ loops when a mass $M$ is placed on the pan. The mass that should be placed on the pan to make it vibrate in $2n$ loops with same frequency (neglect the mass of pan) is

• A. $2M$
• B. $\frac{M}{4}$
• C. $4M$
• D. $\frac{M}{2}$

Answer 1

The correct option is B $\frac{M}{4}$

no of loops $\propto \frac{1}{frequency}$
$\frac{f_1}{f_2}=\sqrt{\frac{T_1}{T_2}}=\sqrt{\frac{m_1}{m_2}}$
$2=\sqrt{\frac{M}{M^1}}$
$\Rightarrow M^1=\frac{M}{4}$