Question

When one metre, one kg and one minute are taken as fundamental units, the magnitude of a force is 36 units. What is the value of this force on CGS system?

• A. ${10}^3$dyne
• B. ${10}^5$dyne
• C. ${10}^6$dyne
• D. ${10}^7$dyne

Answer 1

The correct option is A ${10}^3$dyne

As you know,

Dimension of force $=\left[ML{T}^{-2}\right]$

$\therefore Force=36units=36Kg.m/mi{n}^2$

We know, $1kg={10}^{3}g$

$1m={10}^{2}cm$

$1min=60sec$

Now, force $=\frac{36\left({10}^{3}g\right)\left({10}^{2}cm\right)}{{60sec}^2}$

$=\frac{36\times {10}^5}{3600}g.cm/se{c}^2$

$={10}^{3}g.cm/se{c}^2$

$=1000dyne$ [ because $1g.cm/se{c}^2=1dyne$]

Hence, $Force={10}^{3}dyne$ in CGS.