Question

A $0.5\, kg$ block of brass (density $=8 \times 10^{3} kg \cdot m ^{-3}$ ) is suspended from a string. What is the tension in the string if the block is completely immersed in water ? $\left(g=10\,m \cdot s^{-2}\right)$

• A. $5\, N$
• B. $\frac{0.5}{8 \times 10^{3}} N$
• C. $\frac{5}{8} N$
• D. $\frac{35}{8} N$

Answer 1

Answer: (D)

Mass of block, $m=0.5\, kg$
Density, $\rho=8 \times 10^{3} kgm ^{-3}$
Volume of block,
$V=\frac{m}{\rho}=\frac{0.5}{8 \times 10^{3}}$
$=6.25 \times 10^{-5} m ^{3}$
When block is fully immersed in water, then upthrust force on the block
$F_{1}=m g=V \cdot \rho_{w} \times g$
$=6.25 \times 10^{-5} \times 10^{3} \times 10$
$=0.625\, N$
$\therefore $ Tension in the string
$T=m g-F_{1}$ (upthrust force)
$=0.5 \times 10-0.625=4.375\, N =\frac{35}{8} N$