Question

A rubber ball of mass $10gm$ and volume $15c{m}^3$ dipped in water to a depth of $10m$. Assuming density of water uniform throughout the depth, find
(a) the acceleration of the ball, and
(b) the time taken by it to the surface if it is released from rest. take $g=980cm/s^2$.

• A. (a) $5.9m/s^2$ (b) $2.02$sec.
• B. (a) $4.9m/s^2$ (b) $2.02$sec.
• C. (a) $4.9m/s^2$ (b) $12.02$sec.
• D. (a) $8.9m/s^2$ (b) $2.02$sec.

Answer 1

The correct option is B (a) $4.9m/s^2$ (b) $2.02$sec.

Given,

$m=10gm$

$V=15c{m}^3$

$H=10m$

$g=980cm/s^2$

$\rho =1kg/c{m}^2$

The effective upward force on the ball,

$F=F_B-mg=ma$

$a=\frac{1}{m}(F_B-mg)$

$a=\frac{1}{2}(\rho gh-mg)$

$a=\frac{1}{10}(15\times 1\times 980-10\times 980)$

$a=490cm/s^2=4.9m/s^2$

From the kinematics,

$s=ut+\frac{1}{2}a{t}^2$ initial speed of ball is zero.

$10=\frac{1}{2}\times 4.9\times t^2$

$t=2.02sec$

Thus, the correct option is B.