Question

How much work is done in raising a stone of mass $5Kg$ and relative density $3$ lying at the bed of a lake through height of $3$ meter? (Take $g=10m{s}^{-2}$)

• A. $25J$
• B. $100J$
• C. $75J$
• D. $Noneoftheabove$

Answer 1

Answer: (B)

$100J$

Net force on the stone :=Weight of the stone - buoyant force of water.

Let $d_s,d_w$ be the density of stone and water and V be the volume of the stone.Then:

Buoyant force$=d_W{V}_g$

$W=mg=d_S{V}_g$

$m=d_{S}V$

$F_{net}=V_g(d_S-d_w)=ma=d_S{V}_a$

$a=g(1-\frac{d_w}{d_S})$

$\frac{d_S}{d_w}=3$

$a=10(1-\frac{1}{3})$

Work done=force $\times$ displacement

$=ma\times 3$

$=5\times \frac{20}{3}\times 3=100J$