Find the apparent weight of a metallic block of density $5 \mathrm{~g} \mathrm{~cm}^{-3}$ and dimensions $5…
Find the apparent weight of a metallic block of density $5 \mathrm{~g} \mathrm{~cm}^{-3}$ and dimensions $5 \mathrm{~cm} \times 5 \mathrm{~cm} \times 5 \mathrm{~cm}$, in water.
$5 \times 5 \times 5 \times 5 \mathrm{gf}$
$4 \times 4 \times 4 \times 4 \mathrm{gf}$
$5 \times 4 \times 4 \times 4 \mathrm{gf}$
$4 \times 5 \times 5 \times 5 \mathrm{gf}$
Solution
Density of metallic block,
$
\rho=5 \mathrm{~g} \mathrm{~cm}^{-3}
$
Volume of block,
$
V=5 \mathrm{~cm} \times 5 \mathrm{~cm} \times 5 \mathrm{~cm}
$
Upthrust force on the metallic block in water,
$
\begin{array}{rlr}
F_1 & =m \cdot g & \\
& =\rho_w V \times g & {\left[\rho_w=1 \mathrm{~g} \mathrm{~cm}^{-3}\right]} \\
& =V g=5 \times 5 \times 5 \times g & \\
& =5 \times 5 \times 5 g f &
\end{array}
$
$\therefore$ Apparent weight $=$ Weight of block - Upthrust force
$
\begin{aligned}
& =m g-5 \times 5 \times 5 g f \\
& =(m-5 \times 5 \times 5) g f \\
& =(\rho V-5 \times 5 \times 5) g f \\
& =(5 \times 5 \times 5 \times 5-5 \times 5 \times 5) g f \\
& =5 \times 5 \times 5(5-1) g f \\
& =5 \times 5 \times 5 \times 4 g f
\end{aligned}
$