Laws of Motion — Question 3

(i) The factor on which inertia of a body depends is mass.

More the mass, more is the inertia of the body. Thus, if mass of two bodies is same their inertia will also be same.

Hence, inertia of A and B will be same as mass of both A and B are same.

Hence, ratio of their inertia is 1 : 1

(ii) As we know, momentum of a body (p) = mass (m) x velocity (v)

Given, mass of A and B are equal.

For A,

P_A = mv_A

For B,

P_B = mv_B

Ratio between the two is —

$\dfrac{{\text P}<em>\text A}{\text {P}</em>\text B} = \dfrac{\text m{\text v}<em>\text A}{\text m{\text v}</em>\text B} \\[0.5em]$

As, mass of A = mass of B , hence,

$\dfrac{{\text P}<em>\text A}{{\text P}</em>\text B} = \dfrac{{\text v}<em>\text A}{\text {v}</em>\text B} \\[0.5em]$

Substituting the values, we get,

$\dfrac{{\text P}<em>\text A}{{\text P}</em>\text B} = \dfrac{\text v}{2\text v} \\[0.5em] \Rightarrow \dfrac{{\text P}<em>\text A}{\text {P}</em>\text B} = \dfrac{1}{2} \\[0.5em]$

Hence, ratio between the momentum of A and B is 1 : 2