Question

The kinetic energy of a body is numerically equal to thrice the momentum of the body. Find the velocity of the body.
(A) 2 m/s
(B) 3 m/s
(C) 6 m/s
(D) 9 m/s

Answer 1

We have to use the relation for Momentum and kinetic energy here. Momentum is the product of mass and velocity while kinetic energy expression contains the square of velocity. This can lead to cancellation of the square on one side.
Formula used:
The momentum of the body is given as:
$p = mv$ .
The kinetic energy is given as:
$K.E. = \dfrac{1}{2} mv^2$ .

Complete step-by-step solution:
It is given that the kinetic energy of the body is thrice the momentum. We can write this as:
$\dfrac{1}{2} mv^2 = 3 p$
$\implies \dfrac{1}{2} mv^2 = 3 mv$
The velocity can be obtained from here as:
$v = 6$ m/s.
Therefore the correct answer is option (C).
Additional information:
The kinetic energy and momentum are conserved quantities in elastic collisions. In inelastic collisions, the energies are not conserved. In the conservation law of energy, we consider the terms like kinetic energy and potential energy.

Note: The kinetic energy is expressed in the unit of Joule while the momentum is expressed in terms of kg m/s. Here we are simply equating the magnitudes and we are not equating the units. An equation is said to be dimensionally correct when on the two sides we have all quantities such that the dimensions match everywhere. All the terms should match dimensionally. Therefore, the relation that we have written is not a physical expression but is merely a relation of magnitudes.