Question

A solid cylinder of mass 5 kg is completely submerged into water. What is the tension force in the string supporting the piece of aluminum if the specific gravity of the cylinder’s material is 10? (A) 5 N (B) 0.5 N (C) 50 N (D) 45N​

Answer 1

Given info : A solid cylinder of mass 5 kg is completely submerged into water. What is the tension force in the string supporting the piece of aluminum.

To find : the tension force in the string if the specific gravity of the cylinder's material is 10.

solution : tension in the string = apparent weight of solid cylinder

        now apparent weight of cylinder = weight of cylinder -  force of buoyancy

           = mg - $m_{dis\:water}g$

           = mg - $V\rho_{water}g$

           = mg - $\frac{\rho_{water}mg}{\rho_{solid}}$

           = $mg\left(1-\frac{\rho_{water}}{\rho_{solid}}\right)$

    here, m = 5 kg , g = 10m/s² and specific gravity of material = $\frac{\rho_{solid}}{\rho_{water}}$ = 10

so specific gravity of water , $\frac{\rho_{water}}{\rho_{solid}}$ = 0.1

so apparent weight of cylinder = 5 × 10 (1 - 0.1) = 45 N

therefore the tension in the string supporting the piece of aluminium is 45N