Question

If 'p' is the momentum of an object of 'mass' m, the expression (p^2/2 m) has base units identical to:
(a) Energy
(b) Force
(c) Power
(d) Velocity

Give the solution too.
No span answers.

Answer 1

Answer:

The expression (p^2/2 m) has base units identical to energy i.e. option (a).

Explanation:

First, let's see how energy is given,

$E=\frac{1}{2}mv^2$     (1)

Where,

E=energy of an object

m=mass of an object

v=velocity with which the object is moving

On multiplying and dividing equation (1) with mass  (m) we get;

$E=\frac{1}{2}mv^2\times \frac{m}{m}=\frac{1}{2}\times \frac{m^2v^2}{m}$

$E=\frac{1}{2}\times \frac{m^2v^2}{m}$   (2)

Also, the momentum (P) of a body is given as,

$P=mv$    (3)

By using equation (3) in equation (2) we get;

$E=\frac{1}{2}\times \frac{P^2}{m}=\frac{P^2}{2m}$

Hence, the expression (p^2/2 m) has base units identical to energy i.e. option (a).