Home
Class 12
PHYSICS
A thin, uniform rod of mass M and length...


A thin, uniform rod of mass M and length L is at rest on a smooth horizontal surface. A particle of same mass M collides with the rod at one end perpendicular to its length with velocity `V_(@)` and sticks to it. C is the middle point of the rod and D is a point at a distance of L/4 from end A. the time taken by the rod turn through `90^(@)` after collisions.

A

`(L)/(V_(@))`

B

`(piL)/(V_(@))`

C

`(3piL)/(5V_(@))`

D

`(5piL)/(12V_(@))`

Text Solution

Verified by Experts

The correct Answer is:
D

By COAM about point D (ie about new centre of mass)
`MV_(@)(L)/(4)=[(ML^(2))/(12)+(ML^(2))/(16)+(ML^(2))/(16)]omega`
or `w=(6v_(@))/(5L)`
Now, `t=(theta)/(w)=((pi//2))/(w)=(5piL)/(12v_(@))`
Promotional Banner

Similar Questions

Explore conceptually related problems

A uniform rod of mass m and length L is at rest on a smooth horizontal surface. A ball of mass m, moving with velocity v_0 , hits the rod perpendicularly at its one end and sticks to it. The angular velocity of rod after collision is

A uniform rod AB of mass m and length l at rest on a smooth horizontal surface . An impulse P is applied to the end B . The time taken by the rod to turn through a right angle is :

A uniform rod AB of mass m and length l at rest on a smooth horizontal surface . An impulse P is applied to the end B . The time taken by the rod to turn through a right angle is :

A uniform rod of mass M and length a lies on a smooth horizontal plane. A particle of mass m moving at a speed v perpendicular to the length of the rod strikes it at a distance a/4 from the centre and stops after the collision. Find a. the velocity of the cente of the rod and b. the angular velocity of the rod abut its centre just after the collision.

A uniform rod AB of mass m and length l is at rest on a smooth horizontal surface. An impulse J is applied to the end B , perpendicular to the rod in the horizontal direction. Speed of particlem P at a distance (l)/(6) from the centre towards A of the rod after time t = (pi m l)/(12 J) is.

A uniform rod of mass M and length L, area of cross section A is placed on a smooth horizontal surface. Forces acting on the rod are shown in the digram Ratio of elongation in section PQ of rod and section QR of rod is

A uniform rod lies at rest on a frictionless horizontal surface. A particle, having a mass equal to that of the rod, moves on the surface perpendicular to the rod collides with it, and finally sticks to it. The minimum loss of KE in the collision , under the given conditions, is

A uniform rod of mass m , length l rests on a smooth horizontal surface. Rod is given a sharp horizontal impulse p perpendicular to the rod at a distance l//4 from the centre. The angular velocity of the rod will be

A uniform rod of mass m and length l is suspended about its end. Time period of small angular oscillations is

A uniform rod of length l and mass 2 m rests on a smooth horizontal table. A point mass m moving horizontally at right angles to the rod with velocity v collides with one end of the rod and sticks it. Then