Question

A stone of density $2000kg{m}^{-3}$ 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 $(\rho )=2000kg{m}^{-3}$
Density of water $(\sigma )=1000kg{m}^{-3}$
According to question,
$g^{\prime }=g\left(1-\frac{\sigma }{\rho }\right)$
$g^{\prime }=g\left(1-\frac{1000}{2000}\right)$
$g^{\prime }=g/2....(i)$
We know that,
$S=ut+\frac{1}{2}{g}^{\prime }{t}^2$
$S=\frac{1}{2}{g}^{\prime }{t}^2[\because u=0]$
$S=\frac{1}{2}\times \frac{g}{2}\times (4{)}^2$
$S=\frac{1}{2}\times \frac{(9.8)}{2}\times (4{)}^2$
$S=\frac{9.8\times 16}{4}$
$S=39.2m$