Question

The period of oscillation of the wooden cylinder is $T_0$ in the liquid. If the liquid accelerates up with an acceleration a, the new time period of oscillation will be T, say, Then, T/$T_0$ is equal to:

• A. 1 : 1
• B. g : a
• C. $\sqrt{g:(g+a)}$
• D. none of these

Answer 1

The correct option is C $\sqrt{g:(g+a)}$

The time period of oscillation in a liquid is given by,

$T=2\pi \sqrt{\frac{m}{V{\rho }_{L}g}}$

If $m,V,{\rho }_L$ is constant,

$T\propto \sqrt{g^{-1}}$

In second case $g_{eff}=g+a$

$\frac{T}{T_0}=\sqrt{\frac{(g+a{)}^{-1}}{g^{-1}}}=\sqrt{\frac{g}{g+a}}$

Option $c$ is the correct answer.