Question

In a system of units, the units of mass, length and time are 1 quintal, 1 km and 1 h respectively. In this system 1 N force will be equal to

• A. 1 new unit
• B. 129.6 new unit
• C. 125.7 new unit
• D. ${10}^3$ new unit

Answer 1

Answer: (B)

Key Idea: The product of the numerical value of a physical quantity and its corresponding unit is a constant. Let the numerical value of a physical quantity $p,$ are $n_1$ and $n_2$ in two different systems and the corresponding units are $u_1$ and $u_2,$ then $n_1[u_1]=n_2[u_2]$ Dimensions of force $=[ML{T}^{-2}]$ $\therefore$ $n_1[M_1{L}_1{T}_1^{-2}]=n_2[M_2{L}_2{T}_2^{-2}]$ $\Rightarrow$ $n_2=n_1\left[\frac{M_1}{M_2}\frac{L_1}{L_2}{\left(\frac{T_1}{T_2}\right)}^{-2}\right]$ $n_2=n_1\left[\frac{M_1}{M_2}\frac{L_1}{L_2}{\left(\frac{T_1}{T_2}\right)}^{-2}\right]$ $=1\left[\frac{\text{1}\text{kg}}{1\text{quintal}}\times \frac{1m}{1km}\times {\left(\frac{1s}{1h}\right)}^{-2}\right]$ $=1\left[\frac{1}{100}\times \frac{1}{1000}\times 3600\times 3600\right]$ $=129.6$ new units