The tension in a massles cable connected to an iron ball of 100 kg when it is submerged in sea water is ( `rho_("iron")=8xx10^(3)" kg/m"^(3)` and `rho_("sea water")=1000" kg/m"^(3), g=10" m/s"^(2)`)

Options

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

Answer

C

Explanation

Given, mass of iron ball, `m =100` kg
density of iron ball, `rho_("iron")=8xx10^(3)" kg/m"^(3)`
density of sea water `rho_("sea water")=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 (1- rho_("sea water")/rho_("iron"))=mg(1-1000/(8xx10^(3)))`
`=100xx10(1-1/8)=1000xx7/8=875 N`