Question

In a new system of units, the net force applied on a block of mass $10\, kg$ moving with acceleration $10\, m / s ^{2}$ is given as $100$ unit of force. When the same block is moving at a speed of $20\, m / s$, its kinetic energy become $20$ unit of energy. A liquid has a surface tension of $10\, SI$ units. What is the magnitude of its surface tension in new system? (Dimensional formula of surface tension is $M L^{0} T^{-2}$.)

Answer 1

Let in new system, dimensions be $M, L^{\prime}$ amd $T$
$\therefore$ Given $100\, M ^{\prime} L ^{\prime} T ^{-2}=100\, MLT ^{-2}$ ...(i)
$20\, M ^{1} L ^{12} T ^{-2}=20 \times 100\, ML ^{2} T ^{-2}$ ...(ii)
Solving (i) & (ii); $L ^{\prime}=100\, L$
$\therefore M^{\prime} T^{r-2}=\frac{1}{100} M T^{-2}$
$\therefore 10$ surface tension $\left( MT ^{-2}\right)$ in SI unit
$=10^{3} M ^{1} T ^{-2}$