# A rod  of length  and mass  is kept on a horizontal smooth plane. It is free to rotate and move. A particle of same mass  moving on the plane with velocity  strikes the rod at point  making angle  with the rod. The collision is elastic. After collision, a) The angular velocity of the rod will be 72/55 b) The center of the rod will travel a distance  in the time in which it makes half rotation c) Impulse of the impact force is  d) None of these

## Question ID - 100663 | SaraNextGen Top Answer A rod  of length  and mass  is kept on a horizontal smooth plane. It is free to rotate and move. A particle of same mass  moving on the plane with velocity  strikes the rod at point  making angle  with the rod. The collision is elastic. After collision, a) The angular velocity of the rod will be 72/55 b) The center of the rod will travel a distance  in the time in which it makes half rotation c) Impulse of the impact force is  d) None of these

Answer Key / Explanation : (a,b,c) -

(a,b,c)

The ball has  component of its velocity perpendicular to the length of the rod immediately after collision.  is the velocity of CM of the rod and  is angular velocity of the rod just after collision. The ball strikes the rod with a speed of  in the perpendicular direction and its component along the length of the after the collision is unchanged

Using for the point of collision

Velocity of separation= Velocity of approach

…(i)

Conserving linear momentum (of rod+ particle) in the direction perpendicular to the rod

…(ii)

Conserving angular momentum about point  as shown in the figure

Time taken rotate by  angle,

In the same time, distance travelled =

Using angular impulse- angular momentum equation

[Using impulse-momentum equation on the rod