Home
Class 11
PHYSICS
A uniform rod of mass m and length l res...

A uniform rod of mass `m` and length `l` rests on a smooth horizontal surface. One of the ends of the rod is struck in a horizontal direction at right angles to the rod. As a result the rod obtains velocity `v_(0)`. Find the force with which one-half of the rod will act ont he other in the process of motion.

Text Solution

Verified by Experts


Let `J` be the linear impulse applied at B and `omega` and angular speed of rod
`J=mv_(0)` ..(i) ,brgt `J((l)/(2))=(ml^(2))/(12).omega` .(ii)
solving these two equations
`omega=(6v_(0))/(l)`
Linear speed of D (mid-point of CB) relative C
`v=omega((l)/(4))=(3)/(2)v_(0)`
`therefore` force exerted by upper half on the lower half
`F=(((m)/(2))v^(2))/(((l)/(4)))`
substituting `v=(3)/(2)v_(0)`, we get
`F=(9)/(2)(mv_(0)^(2))/(l)`
Promotional Banner

Topper's Solved these Questions

  • ROTATIONAL MECHANICS

    DC PANDEY|Exercise Level 2 Subjective|36 Videos

  • ROTATION

    DC PANDEY|Exercise (C) Chapter Exercises|39 Videos

  • ROTATIONAL MOTION

    DC PANDEY|Exercise Integer Type Questions|17 Videos

Similar Questions

Explore conceptually related problems

A uniform rod ofmassm and length / rests on a smooth horizontal surface. One of the ends ofthe rod is struck in'a horizontal direction at right angles to the rod. As a result the rod obtains velocity Vq. Findtheforcewithwhich onehalfof the rod will act on the other in the process ofmotion.

A uniform rod of mass m=5.0kg and length l=90cm rests on a smooth horizontal surface. One of the ends of the rod is struck with the impulse J=3.0N*s in a horizontal direction perpendicular to the rod. As a result, the rod obtains the momentum p=3.0N*s . Find the force with which one half of the rod will act on the other in the process of motion.

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 is 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 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 horizontal direction. Speed of the point A of the rod after giving impulse 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 at rest on smooth horizontal surface. An impulse P is applied to end B as shown. Distance travelled by the centre of the rod, while rod rotates by 90^(@)

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 Total elastic potential energy stored in the rod 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