Question

A body of mass $25g$ is under water at a depth of $50cm$. If the specific gravity of material of body is $5$, the work necessary to lift the body slowly to the surface is (Consider $g=9.8\frac{m}{s^2}$ )

• A. $980\times {10}^{5}erg$
• B. $9.8\times {10}^{5}erg$
• C. $980\times {10}^{6}erg$
• D. $98\times {10}^{5}erg$

Answer 1

The correct option is B $9.8\times {10}^{5}erg$


The net force is $F_{net}=weight-Buoyantforce$
$={\rho }_{s}Vg-{\rho }_{w}Vg$
Since specific gravity is $5$
$5=\frac{{\rho }_s}{{\rho }_w}$
${\rho }_w=\frac{{\rho }_s}{5}$
$F_{net}={\rho }_{s}Vg-\frac{{\rho }_{s}Vg}{5}$
$=\frac{4{\rho }_{s}Vg}{5}$
$=\frac{4\times 25\times {10}^{-3}\times 9.8}{5}$
$=196\times {10}^{-3}N$

Work done by this force is
$W=F_{net}\times d$
$=196\times {10}^{-3}\times 50\times {10}^{-2}$
$=9800\times {10}^{-5}J$
$=9.8\times {10}^{5}erg(\because 1J={10}^{7}erg)$