A 1 kg ball moving with a speed of 4 m/s hits obliquely a stationary identical ball inelastically as shown. The first ball moves away at an angle α to the original path. Coefficient of restitution is

Question

A 1 kg ball moving with a speed of 4 m/s hits obliquely a stationary identical ball inelastically as shown. The first ball moves away at an angle α to the original path. Coefficient of restitution is 1/3. The value of α (in degree) is x 0 ​ . The value of 6 x 0 ​ ​ is :

TestHub · Accepted Answer

Resolve the first ball velocity along and perpendicular to the line of centres. The line of centres is at 30° to the initial velocity.

$v_{1 t} = v_{0} sin 3 0^{\circ}$

$v_{1 n} = \frac{v _{0} c o s 3 0 ^{\circ} ( 1 - e )}{2}$

$tan (α + 3 0^{\circ}) = \frac{v _{1 t}}{v _{1 n}}$

$tan (α + 3 0^{\circ}) = \frac{2 t a n 3 0 ^{\circ}}{1 - e}$

$tan (α + 3 0^{\circ}) = 3$

$α + 3 0^{\circ} = 6 0^{\circ}$

$α = 3 0^{\circ}$

$\frac{x _{0}}{6} = \frac{30}{6} = 5$

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JEE Main 2028 (Class 11)