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

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 π √(a b c/g) (B) 8 π √(bc/dg) (C) 2 π √(g/ad) (D) 2 π √(ad/g)

Tardigrade Admin · Accepted Answer

F=-(b c x) × g F=-(b c g) x As F=-k x, Here k=b c g or m=a b c × d T=2 π √(m/k)=2 π √(a b c d/b c g)=2 π √(ad/g)

Q. 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

$2 π \frac{ab c}{g}$

$8 π \frac{b c}{d g}$

$2 π \frac{g}{a d}$

$2 π \frac{a d}{g}$

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

Q. 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

2πgabc​​

8πdgbc​​

2πadg​​

2πgad​​