Question

An unknown metal cube of side $10\text{cm}$ and $\text{RD.}2.6$ is suspended by a thread in a liquid of relative density $1.2$. What will be the tension in the thread?

• A. $1200\text{gf}$
• B. $1400\text{gf}$
• C. $2600\text{gf}$
• D. $2400\text{gf}$

Answer 1

The correct option is B $1400\text{gf}$

Given:
Side of the cube $=l=10\text{cm}$
Volume of aluminium cube $=\text{V}={\text{(side)}}^3=(10{)}^3=1000{\text{cm}}^3$
Relative density of metal $={\text{R.D.}}_{\text{metal}}=2.6$
Relative density of liquid $={\text{R.D.}}_{\text{liquid}}=1.2$
Density of water $=1{\text{g/cm}}^3$
Relative density of metal $=\frac{\text{Density of metal}}{\text{Density of water at}4{}^{\circ }\text{C}}$
Density of metal $={\rho }_{\text{metal}}=2.6{\text{g/cm}}^3$
Mass of metal $=\text{V}\times m=1000\times 2.6=2600\text{g}$
Weight of aluminium cube acting downwards $=2600\text{gf}$
Volume of liquid displaced = Volume of cube $=\text{V}=1000{\text{cm}}^3$
Upthrust due to liquid$=\text{V}\times {\rho }_{\text{liquid}}\times g$
Upthrust due to liquid $=1000\times 1.2\times g=1200\text{gf}$
Tension in the thread $=2600-1200=1400\text{gf}$