Question

In a new system of units, the unit of force is $\text{100 N}$ , unit of length is $\text{10 m}$ and unit of time is $\text{100 s}$ . Unit of mass in this system can be expressed as

• A. $10^{5} \text{ k} \text{g}$
• B. $10^{6} \text{ k} \text{g}$
• C. $10^{2} \text{ k} \text{g}$
• D. $10^{3} \text{ k} \text{g}$

Answer 1

Answer: (A)

Here, force (F) = [MLT^-2] = 100 N ...(i)
Length (L) = [L] = 10 m ...(ii)
Time (t) = [T] = 100 s ...(iii)
Substituting values of L and T from Equations. (ii) and (iii) in Equation. (i), we get
M × 10 × (100)^-2 = 100
or $\frac{M \times 1 0}{1 0 0 \times 1 0 0} = 1 0 0$
or M = 100 × 1000 kg
$\text{M} = 10^{5 \, } \text{kg}$