Question

A metallic sphere weighting 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 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 correct option is D 27.6 N

This question is about equilibrium through which we could find the tension in the string. Equilibrium is a type of condition in which all the forces are balanced in a given system or surrounding.

In this question, we have been given a mass where four forces which are balanced. We will be using the condition of equilibrium.

Weight$=m=3kg$

$Density=\rho =0.8$

$Relativedensity=\sigma =10$

Tension of the string$=T$

Taking gravitational force$=g=10$

For equilibrium :

$T+Fₐ=Weight$

Here,

$F_a=\rho \times V\times g$

Weight$=\sigma \times V\times g$

now,

$T=V\times g\times [1-(\sigma /\rho \left)\right]$

$T=m\times g\times [1-(\sigma /\rho \left)\right]$

$T=3\times 10\times [1-(0.8/10\left)\right]$

$T=30\times 0.92$

$T=27.6Newtons$

Hence,

option $D$ is correct answer.