Question

The tension in a massless cable connected to an iron ball of $100\, kg$ when it is submerged in sea water is $\left(\rho_{\text {iron }}=8 \times 10^{3} \,kg / m ^{3}\right.$ and $\left.\rho_{\text {sea water }}=1000\, kg / m ^{3}, \,g=10 \,m / s ^{2}\right)$

• A. 950 N
• B. 846 N
• C. 875 N
• D. 933 N

Answer 1

Answer: (C)

Given, mass of iron ball, $m=100 \,kg$
density of iron ball, $\rho_{\text {iron }}=8 \times 10^{3} \,kg / m ^{3}$
density of sea water $\rho_{\text {sea wate }}$ $=1000 \,kg / m ^{3}$
and acceleration due to gravity, $g=10\, m / s ^{2}$
When the ball is submerged in sea water, then upthrust force acting on the ball in upward direction. When the ball is completely submerged, it's effective weight gets decreased. This decrease in weight would be equal to the upthrust on the body according to Archimedes principle. Hence tension $T$ in the massless cable is equal to the apparent weight on the ball.
i.e., $T=$ apparent weight
$T=W\left(1-\frac{\rho_{\text {sea water }}}{\rho_{\text {iron }}}\right)=m g\left(1-\frac{1000}{8 \times 10^{3}}\right)$
$=100 \times 10\left(1-\frac{1}{8}\right)=1000 \times \frac{7}{8}=875 \,N$