Home
Class 11
PHYSICS
A uniform circular disc has radius R and...


A uniform circular disc has radius `R` and mass `m`. A particle, also of mass `m`, if fixed at a point A on the edge of the disc as shown in the figure. The disc can rotate freely about a horizontal chord PQ that is at a distance `R//4` from the centre `C` of the disc. The line AC is perpendicular to `PQ`. Initially the disc is held vertical with the point A at its highest position. it is then allowed to fall, so that it starts rotation about PQ. Find the linear speed of the particle as it reaches its lowest position.

Text Solution

Verified by Experts

During the fall the disc mas system gains rotational kinetic energy. This is the expense of potential energy.

Applying conservation of mechanical energy, we get
Initial total energy `=` Final total energy
`mg(2R+(2R)/4)+mg(R+(2R)/4)=mgR+1/2Iomega^(2)`
where `I=MI` of the disc mass system about `PQ`
`=mg+(10R)/4+mg(6R)/4=mgR+1/2omega^(2)`
`implies 3mgR=1/2IOmega^(2)`
`implies w=(sqrt(6mgR)/1)`...........i
`(I)_(PQ)=(I_("disc"))_(PQ)+(I_("mass"))_(PQ)`
`=[(mR^(2))/4+M(R/4)2]+m((5R)/4)^(2)`
[Therfore `MI` of disc about the diameter `=(1/4)MR^(2)`]
`=(mR^(2)[4+1+25])(15mR^(2))/8`...........ii
Form eqn i and ii `omega=sqrt((6mgRxx8)/(15mR^(2)))=sqrt((16g)/(5R))`
Let `v` be velocity of mass `m` at the lowest point of rotation
`v=omega(R+R/4)`
`=sqrt((16g)/5g)xx(5R)/4=sqrt(5gR)`
Promotional Banner

Topper's Solved these Questions

  • RIGID BODY DYNAMICS 2

    CENGAGE PHYSICS|Exercise Solved Examples|12 Videos

  • RIGID BODY DYNAMICS 2

    CENGAGE PHYSICS|Exercise Exercise 3.1|11 Videos

  • RIGID BODY DYNAMICS 1

    CENGAGE PHYSICS|Exercise Integer|11 Videos

  • SOUND WAVES AND DOPPLER EFFECT

    CENGAGE PHYSICS|Exercise Integer|16 Videos

Similar Questions

Explore conceptually related problems

A uniform circula disc has radius R and mass m. A particle also of mass m, is fixed at a point A on the edge of the disc as shown in figure. The disc can rotate freely about a fixed horizontal chord PQ that is at a distance R/4 from the centre C of the disc. The line AC is perpendicular to PQ. Initially, the disc is held vertical with the point A at its highes position.

A uniform circular disc has radius R and mass m . A particle also of mass m is fixed at a point A on the wedge of the disc as in fig. The disc can rotate freely about a fixed horizontal chord PQ that is at a distance R//4 from the centre C of the disc. The line AC is perpendicular to PQ . Initially the disc is held vertical with the point A at its highest position. It is then allowed to fall so that it tarts rotating about PQ . Find the linear speed of the particle at it reaches its lowest position. .

The moment of inertia of a uniform circular disc of radius R and mass M about an axis passing from the edge of the disc and normal to the disc is.

A quarter disc of radius R and mass m is rotating about the axis OO' (perpendicular to the plane of the disc) as shown. Rotational kinetic energy of the quarter disc is

A disc has mass 9 m. A hole of radius R/3 is cut from it as shown in the figure. The moment of inertia of remaining part about an axis passing through the centre 'O' of the disc and perpendicular to the plane of the disc is :

A disc of mass M and radius R can rotate freely in a vertical plane about a horizontal axis at O distance r from the centre of the disc as shown in Fig. The disc is released from rest in the shown position. Answer the following questions based on the above information The angular velocity of the disc in the above described case is

A disc of mass M and radius R can rotate freely in a vertical plane about a horizontal axis at O distance r from the centre of the disc as shown in Fig. The disc is released from rest in the shown position. Answer the following questions based on the above information Reaction force exerted by the hinge on the disc at this instant is

A disc of a mass M and radius R can rotate freely in vertical plane about a horizontal axis at O . Distant r from the centre of disc as shown in the figure. The disc is released from rest in the shown position. The angular acceleration of disc when OC rotates by an angles of 37^(@) is