Question

A block of steel of size $5 \times 5 \times 5\, cm ^{3}$ is weighed in water. If relative density of steel is $7$, its apparent weight is

• A. $6 \times 5 \times 5 \times 5\, g\, wt$
• B. $4 \times 4 \times 4 \times 7\, g\, wt$
• C. $5 \times 5 \times 5 \times 7\, g\, wt$
• D. $4 \times 4 \times 4 \times 6\, g\, wt$

Answer 1

Answer: (A)

Apparent weight $=\rho_{s} v_{b} g-\rho_{w} v_{b} g$
$=v_{b} g\left(\rho_{s}-\rho_{w}\right)$
$=5 \times 5 \times 5 \times g \times(7-1)$
$\left[\rho_{w}=1 \rho_{s}=7\text{(given)}\right.$
$=6 \times 5 \times 5 \times 5 \times g\, wt$
Where, $\rho _{s}$ - density of steel
$\rho_{w}$-density of water
$v_{b}$ - volume of block
(side $\times$ side $\times$ side)