Two bodies A and B of the same mass are moving with velocities v and 3v respectively. Compare their (a) inertia (b) Momentum (c) the force needed to stop them in the same time.

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Solution

(a) Since inertia is a measure of mass which is same for both bodies, so the ratio of inertia for two bodies will be $\frac{1}{1}$

(b) Momentum
$P = m \times v$
$P_{1} = m \times v = m v$
$P_{2} = m \times 3 v$

$\frac{P_{1}}{P_{2}} = \frac{m v}{3 m v} = \frac{1}{3}$

(c) Force
$F \times T = M o m e n t u m$

$F = \frac{M o m e n t u m}{T}$
$F_{1} = \frac{1}{1}$

$F_{2} = \frac{3}{1}$

$\frac{F_{1}}{F_{2}} = \frac{1}{3}$

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Two bodies A and B of the same mass are moving with velocities v and 3v respectively. Compare their (a) inertia (b) Momentum (c) the force needed to stop them in the same time.

(a) Since inertia is a measure of mass which is same for both bodies, so the ratio of inertia for two bodies will be 11(b) MomentumP=m×vP1=m×v=mvP2=m×3vP1P2=mv3mv=13(c) ForceF×T=MomentumF=MomentumTF1=11F2=31F1F2=13