Home
Class 12
PHYSICS
A cylinder of mass m rests on a supporti...

A cylinder of mass m rests on a supporting block as shown. If `beta=60^(@) " and " theta=30^(@)`, calculate the maximum acceleration 'a' which the block may be given up the incline so that the cylinder does not lose contact at B. (neglect friction anywhere).

Text Solution

Verified by Experts

`(sqrt(3)N_(1))/(2)-(mg)/(2)-(N_(2)sqrt(3))/(2)=ma`
`(sqrt(3)N_(1))/(2)-(sqrt(3)N_(2))/(2)=ma+(mg)/(2)`.....(`i`)
`rArr (N_(1)+N_(2))/(2)=(mgsqrt(3))/(2)`
`rArr (sqrt(3)N_(1))/(2)+(sqrt(3)N_(2))/(2)=(3mg)/(2)`….. (`ii`)
From equation (`i`) and (`ii`), we have
`sqrt(3)N_(1)=2mg+ma`, `sqrt(3)N_(2)=mg-ma`
Since cylinder does not losse the contact, so `N_(1) ge 0`, `N_(2) ge 0`
`rArr a le g`
`rArr a_(max)=g`
Promotional Banner

Similar Questions

Explore conceptually related problems

A block of mass m is placed on the top of another block of mass M as shown in the figure. The coefficient of friction between them is mu . The maximum acceleration with which the block M may move so that m also moves along with it is

A block of mass 1.0 kg rests on a wedge of angle theta . The acceleration which should be given to the wedge so that the block falls freely is :

A block is kept on a smooth inclined plane of angle of inclination theta that moves wuth a contact acceleration so that the block does not slide relative to the inclined plane. If the inclined plane stops the normal contact force offered by the plane on the block changes by a factor

A block of mass 2 kg rests on an inclined plane of inclination angle 37^(@) , then calculate the force of friction acting on the block [ take g = 10 m//s^(2))

A system consists of block A and B each of mass m connected by a light spring as shown in the figure with block B in contact with a wall. The block A compresses the spring by 3mg/k from natural length of spring and then released from rest. Neglect friction anywhere. Velocity of centre of mass of system comprising A and B when block B just loses contact with the wall

Consider a cylinder of mass M resting on a rough horizontal rug that is pulled out from under it with acceleration 'a' perpendicular to the axis of the cylinder. What is F_("friction") at point P ? It is assumed that the cylinder does not slip.

The coefficient of static friction between a block of mass m and an incline is mu_s=0.3 , a. What can be the maximum angle theta of the incline with the horizontal so that the block does not slip on the plane? b. If the incline makes an angle theta/2 with the horizontal, find the frictional force on the block.

In which of the following cases the magnitude of acceleration of the block A will be maximum (neglecting friction, mass of pulley and string)

In which of the following cases the magnitude of acceleration of the block A will be maximum (neglecting friction, mass of pulley and string)

A block of mass m is at rest on the another blcok of same mass as shown in figure. Lower block is attached to the spring then the maximum amplitude of motion so that both the blcok will remain in contact is