Home
Class 12
PHYSICS
In the adjacent figure ABC is a uniform ...

In the adjacent figure `ABC` is a uniform isosceles triangular lamina of mass `m` and `AB=AC=l`.
The lamina is free to rotate about a fixed horizontal axis `OAO'` which is in the plane of the lamina. Initially the lamina is in static equilibrium with maximum gravitational potential energy. Due to slight disturbance, lamina starts rotating. Now choose the correct option (s)

A

The maximum angular speed acquired by lamina is `4sqrt((sqrt(2)g)/(3l))`

B

The maximum vertical force on the axis by the lamina is `41/9mg`

C

Angular momentum of the lamina about `OAO'` is conserve

D

When the lamina acquire maximum angular speed acceleration of centre of mass is zero

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
`:'-DeltaU=DeltaK`
`(2sqrt(2)mgl)/3=1/2.(ml^(2)omega^(2))/4`
`( "moment of inertia about" OAO'=(ml^(2))/4)`
`impliesomega=sqrt(16sqrt(2))/3.g/l=4sqrt((sqrt(2)g)/(3l))`
`F-mg=momega^(2)R=mxx(16sqrt(2)g)/(3l).(sqrt(2)l)/3`
`impliesF+mg+(32mg)/9-(41mg)/9`
Promotional Banner

Similar Questions

Explore conceptually related problems

Find MI of a triangular lamina of mass M about the axis of rotation AB shown in Fig.

A right triangular plate ABC of mass m is free to rotate in the verticle plane about a fixed horizontal axis through A. It is supported by a string such that the side AB is horizontal. The reaction at the support A is

A right triangular plate ABC of mas m is free to rotate in the vertical plane about a fixed horizontal axis through A . It is supported by a string such that the side AB is horizontal. The reaction at the support A is : .

ABC is a triangular framwork of three uniform rods each of mass m and length 2l . It is free to rotate in its own plane about a smooth horizontal axis through A which is perpendicular to ABC. If it is released from rest when AB is horizontal and C is above AB. Find the maximum velocity of C in the subsequent motion.

In the figure shown one end of a light spring of natural length l_(0)=sqrt(5/8)m(~~0.8m) is fixed at point D and other end is attached to the centre B of a uniform rod AF of length l_(0)//sqrt(3) and mass 10kg. The rod is free to rotate in a vertical plane about a fixed horizontal axis passing through the end A of the rod. The rod is held at rest in horizontal position and the spring is in relaxed state. It is found that, when the rod is released to move it makes an angle of 60^(@) with the horizontal when it comes to rest for the first time. Find the (a) the maximum elogation in the spring . (Approximately) (b) the spring constant. (Approximately)

In the adjoining figure along which axis the M.I. of the triangular lamina will be maximum- [Given that AB=3 cm, BC =4 cm, AC=5 cm]

A thin rod of mass m and length l is free to rotate on a smooth horizontal plane about its one fixed end. When it is at rest, it receives a horizontal impulse J at its other end, at angle of 37^(@) with the length. Choose incorrect option immediately after impact:

A uniform rod of length l , mass m , cross-sectional area A and Young's modulus Y is rotated in horizontal plane about a fixed vertical axis passing through one end, with a constant angular velocity omega . Find the total extension in the rod due to the tension produced in the rod.

A uniform rod AB of length 2l and mass m is rotating in a horizontal plane about a vertical axis through A, with angular velocity omega , when the mid-point of the rod strikes a fixed nail and is brought immediately to rest. Find the impulse exerted by the nail.