Question

A piece of wood has dimensions $a, b$ and $c$ Its relative density is $d$. It is floating in water such that the side $a$ is vertical. It is now pushed down gently and released. The time period is

• A. $2 \pi \sqrt{\frac{a b c}{g}}$
• B. $8 \pi \sqrt{\frac{bc}{dg}}$
• C. $2 \pi \sqrt{\frac{g}{ad}}$
• D. $2 \pi \sqrt{\frac{ad}{g}}$

Answer 1

Answer: (D)

$ F=-(b c x) \times g$
$F=-(b c g) x$
As $F=-k x,$ Here $k=b c g$ or $m=a b c \times d$
$T=2 \pi \sqrt{\frac{m}{k}}=2 \pi \sqrt{\frac{a b c d}{b c g}}=2 \pi \sqrt{\frac{ad}{g}}$