Question

Write the dimensional formula of Force.
(A) $MLT$
(B) $ML{T^{ - 2}}$
(C) $ML{T^{ - 2}}$
(D) None of the above

Answer 1

The force is the derived quantity. Use Newton's second of motion to find the dimension of the force. Substitute the dimension of the mass and the acceleration in the formula and simplification of it provides the dimension of the force.

Useful formula:
The formula of the force is given by

$F = ma$

Where $F$ is the force, $m$ is the mass of the body under consideration and $a$ is the acceleration of the body.

Complete step by step solution:
Force is the push or pull that acts on the object. It may or may not cause the movement or retards the movement. It is of two types as balanced force and the unbalanced force. If the forces of the body do not cause any change in the rest or the motion of the body, it is known as balanced force. If it causes any change in the state, then it is an unbalanced force. This concept was explained by Newton’s first law of motion.
Let us consider the formula of the force
$F = ma$
The unit of the mass is $Kg$ and so its dimension is $M$ . The unit of the acceleration is $m{s^{ - 2}}$ and its dimension is given as $L{T^{ - 2}}$ .The product of these two dimensions provides the physical dimensions of the force.
$F = M \times L{T^{ - 2}}$
$F = ML{T^{ - 2}}$
Hence the physical dimensions of the force is obtained as $ML{T^{ - 2}}$ .

Thus the option (B) is correct.

Note: The physical dimension of the acceleration is obtained from the formula acceleration is the ratio of the velocity and the time taken. The dimension of the velocity is $L{T^{ - 1}}$ and the dimension of the time taken is $T$ . Hence the dimension of the acceleration is $L{T^{ - 2}}$ .