Ncert Exercises & Solutions

30. If the unit of force is 100 N, the unit of length is 10 m, and the unit of time is 100 sec, what is the unit of mass in this system of units?

Hint: Use the concept of conversion of units.

Step 1: Write the dimensions of F.

$\begin{array}{l} Dimension of force F = [{MLT}^{- 2}] = 100 N . . . . . . (i) \\ Length (L) = [L] = 10 m . . . . . . . . (ii) \\ Time (t) = [T] = 100 s . . . . . . . . (iii) \end{array}$

Step 2: Find the value of M in the new system.

Substituting values of L and T from Eqs. (ii) and (iii) in Eq. (i), we get,

$M \times 10 \times (100)^{- 2} = 100$
$\Rightarrow \frac{M \times 10}{100 \times 100} = 100$
$\Rightarrow M = 100 \times 1000 kg$
$M = 10^{5} kg$

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