# Two equal spheres  and , each of mass , are in contact on a smooth horizontal table. A third sphere  of same size as that of  or  but mass  impinges symmetrically on them with a velocity  and is itself brought to rest The coefficient of restitution between the two spheres  and  (or between  and ) is a) b) c) d)

## Question ID - 101219 :- Two equal spheres  and , each of mass , are in contact on a smooth horizontal table. A third sphere  of same size as that of  or  but mass  impinges symmetrically on them with a velocity  and is itself brought to rest The coefficient of restitution between the two spheres  and  (or between  and ) is a) b) c) d)

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Answer Key : (a) -

(a)

velocity of sphere  before impact. As the spheres are identical, the triangle  formed by joining their centres is equilateral. The spheres  and  will move in direction  and after impact making an angle of  with the original lines of motion of ball

Let  be the speed of the ball  and  after impact

Momentum conservation gives

(i)

From Newton’s experimental law, for an oblique collision, we have to take components along normal, i.e., along  for balls  and

Combining Eqs. (i) and (ii), we get

Next Question :

A pendulum consists of a wooden bob of mass  and length . A bullet of mass is fired towards the pendulum with a speed . The bullet emerges immediately out of the bob from the other side with a speed of  and the bob starts rising. Assume no loss of mass of bob takes place due to penetration

 What is the momentum transferred to the bob by the bullet? a) b) c) d)