Question

A metallic sphere of mass 3 kg in air is held by a string so as to be completely immersed in a liquid of relative density 0.8. The relative density of metallic sphere is 10. The tension in the string is :-

A. 18.7 N
B. 42.5 N
C. 32.7 N
D. 27.6 N

Answer 1

The tension in the string is determined as 27.6 N. (Option D).

How to calculate the tension in the string?

The tension in the string is calculated by applying the following formula.

Tension in string = Weight in air - Buoyant force

T = γVg - ρVg

where;

• m is the mass of the sphere
• V is the volume of the sphere
• ρ is the density of the liquid
• γ is the relative density

The equation above is simplified as follows;

T = Vg(γ - ρ)

The tension in the string is calculated as;

T = mg(1 - γ/ρ)

T = 3 x 10 (1 - 0.8 / 10)

T= 30 x (1 - 0.08)

T = 30 x 0.92

T = 27.6 N