Question

A stone of density $2000\, kg\, m^{-3}$ completely immersed in a lake is allowed to sink from rest. If the effect of friction is neglected, then after $4$ seconds, the stone will reach depth of

• A. 78.4 m
• B. 39.2 m
• C. 19.6 m
• D. 9.8 m
• E. 24.6 m

Answer 1

Answer: (B)

Given, density of stone $(\rho)=2000\,kg\,m ^{-3}$
Density of water $(\sigma)=1000\,kg\,m ^{-3}$
According to question,
$g'=g\left(1-\frac{\sigma}{\rho}\right) $
$g'=g\left(1-\frac{1000}{2000}\right) $
$g'=g / 2 \,....(i)$
We know that,
$S=u t+\frac{1}{2} g^{\prime} t^{2} $
$S=\frac{1}{2} g^{\prime} t^{2} [\because u=0] $
$S=\frac{1}{2} \times \frac{g}{2} \times(4)^{2} $
$S=\frac{1}{2} \times \frac{(9.8)}{2} \times(4)^{2} $
$S=\frac{9.8 \times 16}{4} $
$S=39.2\,m$