Question

What is the CGS unit of force?
A. N
B. Nm
C. dyne
D. dyne.cm

Answer 1

Hint: Force acting on the body is defined to be the product of the mass and the acceleration of the body on which the force is acting. One can find the CGS unit of force by knowing the dimensional formula of force.

Complete step by step answer:
Force is a physical quantity which is said to be equal to the product of the mass and the acceleration of a body on which the force is acting.If we want to express force mathematically, then it is given as $F=ma$, where F is the force acting on the body, m is the mass of the body and a is the acceleration of the body.
Now, since magnitude of force is equal to product of mass and acceleration, its dimensional formula is equal to the product of dimensional formulae of mass and acceleration.
Hence, the dimensional formula of force is equal to,
$\left[ F \right]=\left[ M \right]\left[ L{{T}^{-2}} \right]\\
\Rightarrow \left[ F \right] =\left[ ML{{T}^{-2}} \right]$
We know that the CGS unit of mass, length and time are gram (g), centimetre (cm) and second (s) respectively. Therefore, the CGS unit of force will be equal to $gcm{{s}^{-2}}$.And the CGS unit of force (i.e. $gcm{{s}^{-2}}$) is called dyne I.e. $1dyne=1gcm{{s}^{-2}}$ .

Therefore, the correct option is C.

Note: force and acceleration are vector quantities. A body accelerates only when there is a net unbalanced force applied on it and the direction of acceleration of the body is along the direction of the applied force. N (newton) is the SI unit of force. Nm is the SI unit of energy or work done on a body. dyne.cm is the CGS unit of energy or work done.