Home
Class 11
PHYSICS
A uniform bar of length 6a and mass 8m l...

A uniform bar of length `6a` and mass `8m` lies on a smooth horizontal table. Two point masses `m` and `2m` moving in the same horizontal plane with speeds `2v` and `v` respectively, strike the bar (as shown in figure) and stick to the bar after collision. Calculate (a) velocity of the centre of mass (b) angular velocity about centre of mass and (c) total kinetic energy, just after collision.

Text Solution

Verified by Experts

(a) As `F_(ext)=0` linear momentum of the system is conserved i.e., `-2mxxv+mxx2v+0=(2m+m+8m)xxV`
or `V=0` i.e., velocity of centre of mass is zero.
(b) As `tau_(ext)=0` angular momentum of the system is conserved. i.e,
`m_(1)v_(1)r_(1)+m_(2)v_(2)r_(2)=(I_(1)+I_(2)+I_(3)) omega`
`2mva+m(2v)(2a)=[2m(a)^(2)+8mxx(6a)^(2)//12]omega`
ie. `6mva=30ma^(2) omegarArromega=(v/(5a))`
(c) From (a) and (b) it is clear that, the system has no translatory motion but only rotatory motion.
`E=1/2Iomega^(2)=1/2(30ma^(2))[v/(5a)]^(2)=3/5mv^(2)`
Promotional Banner

Similar Questions

Explore conceptually related problems

A uniform bar of length 6a and mass 8 m lies on a smooth horizontal table. Two point-masses m and 2m moving in the same horizontal plane with speeds 2v and v respectively strike the bar as shown in Fig, and stick to the bar after collision.

A uniform bar of length 6a and mass 8m lies on a smooth horizontal table. Two point masses m and 2m moving in the same horizontal plane with speeds 2v and v , respectively, strike the bar (as shown in the figure) and stick to the bar after collision. Denoting angular velocity (about the centre of mass), total energy and centre of mass velocity by omega , E and V_(C) , respectively, we have after collision

A uniform bar of length 6a and mass 8m lies on a smooth horizontal table. Two point masses m and 2m moving in the same horizontal plane with speed 2v and v, respectively, strike the bar [as shown in the fig.] and stick to the bar after collision. Denoting angular velocity (about the centre of mass), total energy and centre of mass velocity by omega , E and v_c respecitvely, we have after collison

A thin uniform bar of length L and mass 8m lies on a smooth horizontal table .Two point masses m and 2 m are moving in the same horizontal plane from opposite sides of the bar with speeds 2v and v respectively .The masses stick to the bar after collision at a distances (L)/(3) and (L)/(6) respectively from the center of the bar if the bar starts rotating about its center of mass as result of collision the angular speed of the bar will be

A uniform rod of length lambda lies on a smooth horizontal table A particle moving on the table has a mass m and a speed v before the collision and it sticks to the rod after the collision. The rod has a mass M then find out. The velocity of the centre of mass C and the angular velocity of the system about the centre of mass after the collision.

A uniform rod of length L lies on a smooth horizontal table. The rod has a mass M . A particle of mass m moving with speed v strikes the rod perpendicularly at one of the ends of the rod sticks to it after collision. Find the velocity of the centre of mass C and the angular, velocity of the system about the centre of mass after the collision.

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

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