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 in CGS system?

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

Answer 1

Answer: (A)

As you know,
Dimension of force $=\left[ML{T}^{-2}\right]$
$\therefore$ F orce $=36$ units $=36Kg\cdot m/mi{n}^2$
We know, $1kg=10^{3}g$
$1m=10^{2}cm$
$1min=60sec$
Now, force $=\frac{36\left(10^{3}g\right)\left(10^{2}cm\right)}{60se{c}^2}$
$=\frac{36\times 10^5}{3600}g\cdot cm/se{c}^2$
$=10^{3}g\cdot cm/se{c}^2$
$=1000$ dyne [ because $1g\cdot cm/se{c}^2=1$ dyne]
Hence, $F$ orce $=10^3$ dyne in CGS.