Question

Essential characteristic of equilibrium is:-
(A) Momentum equal zero
(B) Acceleration equals zero
(C) $K.E$ equals zero
(D) Velocity equals zero

Answer 1

The body is said to be in equilibrium if it is the position of the rest or of the uniform motion. The uniform motion implies that the change in the velocity is zero. This equilibrium condition is obtained when no force is applied on the body or else the constant force is applied.

Useful formula:
(1) The formula of the kinetic energy is given as

$K.E = \dfrac{1}{2}m{v^2}$

Where $K.E$ is the kinetic energy, $m$ is the mass of the considered body under the equilibrium and $v$ is the velocity of the body.

(2) The formula of the acceleration is given as

$a = \dfrac{{dv}}{{dt}}$

Where $a$ is the acceleration of the body, $dv$ is the change in the velocity and the $dt$ is the time taken.

Complete step by step solution:
The equilibrium is the condition in which the body is in stable condition such that it can be either in a state of rest or of uniform motion. From the above point, it is clear that the equilibrium also occurs in the motion. Hence the motion need not be the zero and for the motion the kinetic energy is also required. Hence the kinetic energy is also not equal to zero. Let us take the formula of the kinetic energy,

$K.E = \dfrac{1}{2}m{v^2}$

For the motion, the kinetic energy is non zero, hence

$\dfrac{1}{2}m{v^2} \ne 0$

From the above step, we can also say

$v \ne 0$

Hence the velocity of the body under equilibrium in the motion is not equal to zero. The acceleration is the change in the velocity of the body. The body is said to be in the equilibrium, if it has the uniform velocity. This means that the change in the velocity will be zero. Let us consider the equation of the acceleration,

$a = \dfrac{{dv}}{{dt}}$

For uniform velocity, $dv = 0$

$a = 0$

Hence for the equilibrium, the acceleration must be zero.

Thus the option (B) is correct.

Note: This equilibrium condition is explained by Newton's first law of motion. It says that the body remains in its state of rest or of uniform motion until the unbalanced force is applied on it. The kinetic energy is substituted as zero, since the presence of kinetic energy denotes that the body is in motion.