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

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

• Option 1)

1/9

• Option 2)

8/9

• Option 3)

4/9

• Option 4)

5/9

Views

$(4m)U = ( 4 M ) V_1 + 2 mv_2 = 4 U = 4 V_1 + 2 V_2 \\\\ e = 1 = \frac{- ( V_2- V_1 )}{(0-u )}\\\\ V_2 - V_1 = U \\\\ 4 V_2 - 4 V_1 = 4 U \\\\ 4 V_1 + 2 V_2 = 4 U \\\\ -------\\\\ 6 V_2 = 8 V \\\\ V_2 = 4/3 U$

$V_1 = V_2 - U \\\\ = ( \frac{4}{3} -1 ) U \\\\ ( V_1 = \frac{1}{3} U ) \\\\ for \: \: A \\\\ K_ i = \frac{1}{2}mU^2 \\\\ K_ f = \frac{1}{2}mv_1 ^ 2 = \frac{1}{2} m ( \frac{1}{9} U^2 ) \\\\ \frac{\Delta KE }{K _ i O } = \frac{ \frac{1}{2} mU^2 ( 1-1/9)}{\frac{1}{2} mU^2 } \\\\ fraction = 8/9$

Option 1)

1/9

Option 2)

8/9

Option 3)

4/9

Option 4)

5/9

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