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