• # question_answer An U tube of uniform bore of cross-sectional area A is set up vertically with open ends up. A liquid of mass M and density d is poured into it. The liquid column will oscillate with a period A)  $2\pi \,\sqrt{\frac{M}{g}}$               B)  $2\pi \,\sqrt{\frac{MA}{dg}}$ C)  $2\pi \,\sqrt{\frac{M}{Adg}}$                       D)  $2\pi \,\sqrt{\frac{M}{2Adg}}$

$\Rightarrow$where L is the length of the liquid is one of the limbs. However, if L is taken to be the length of the liquid column, then length of liquid in each limb is $\frac{n'}{n}=\frac{v}{v-{{v}_{s}}}$. $\frac{\Delta n}{n}=\frac{{{v}_{s}}}{v-{{v}_{s}}}$       $\frac{2.5}{100}=\frac{{{v}_{s}}}{320-{{v}_{s}}}=\frac{1}{40}$ $40{{v}_{s}}=320-{{v}_{s}}$       ${{v}_{s}}=\frac{320}{41}\simeq 8\,m/s$ $V=\frac{1}{4\pi {{\varepsilon }_{0}}}\left[ \frac{Q}{R} \right]+\frac{1}{4\pi {{\varepsilon }_{0}}}\left[ \frac{q}{r} \right]$     $=\frac{1}{{{\varepsilon }_{0}}}\left[ \frac{Q}{4\pi {{R}^{2}}}\times R+\frac{q}{4\pi {{r}^{2}}}\times r \right]$