Body A of mass 4m moving with speed u collides with another body B of mass 2m, at rest. The collision is head on and elastic in nature. After the collision the fraction of energy lost by the colliding body A is :

Question

Body A of mass 4m moving with speed u collides with another body B of mass 2m, at rest. The collision is head on and elastic in nature. After the collision the fraction of energy lost by the colliding body A is : (A) (4/9) (B) (5/9) (C) (1/9) (D) (8/9)

Tardigrade Admin · Accepted Answer

Fractional loss of KE of ccolliding body (Δ KE/KE) = (4(m1m2)/(m1 + m2)2) = (4(4m)2m/(4m+2m)2) = (32m2 /36m2) = (8/9)

Q. Body A of mass 4m moving with speed u collides with another body B of mass 2m, at rest. The collision is head on and elastic in nature. After the collision the fraction of energy lost by the colliding body A is :

$\frac{4}{9}$

$\frac{5}{9}$

$\frac{1}{9}$

$\frac{8}{9}$

Fractional loss of KE of ccolliding body
$\frac{Δ K E}{K E} = \frac{4 ( m _{1} m _{2} )}{( m _{1} + m _{2} ) ^{2}}$
$= \frac{4 ( 4 m ) 2 m}{( 4 m + 2 m ) ^{2}}$
$= \frac{32 m ^{2}}{36 m ^{2}} = \frac{8}{9}$