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 of the colliding body A is :

# 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 of the colliding body A is :

1. A

$\frac{4}{9}$

2. B

$\frac{5}{9}$

3. C

$\frac{1}{9}$

4. D

$\frac{8}{9}$

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### Solution:

Fractional loss of KE colliding body
$\begin{array}{l}\frac{\mathrm{\Delta KE}}{\mathrm{KE}}=\frac{4\left({\mathrm{m}}_{1}{\mathrm{m}}_{2}\right)}{{\left({\mathrm{m}}_{1}+{\mathrm{m}}_{2}\right)}^{2}}=\frac{4\left(4\mathrm{m}\right)2\mathrm{m}}{\left(4\mathrm{m}+2\mathrm{m}{\right)}^{2}}\\ =\frac{32{\mathrm{m}}^{2}}{36{\mathrm{m}}^{2}}=\frac{8}{9}\end{array}$  +91

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