Home
Class 12
PHYSICS
A sphere of mass m is placed on a rough ...

A sphere of mass m is placed on a rough surface of coefficient of friction `mu`. Initially the sphere is given a velocity `v_(0)` and angular velocity `omega_(0)` as shown in figure. Find out the value of `omega_(0)` so that the sphere will come to rest after a certain time. Sphere has radius r.

Text Solution

Verified by Experts


Let at time t it spops.
Then at time t
`v_(0) - mu g t = 0" "(a = - mu "g as sphere skids")`
`t = v_(0)//mu g`
Also, `- mu m g r = (2)/(5) mr^(2) alpha`
`alpha = -(5)/(2) (mu g)/(r)`
`omega = omega_(0) - (5)/(2)(mu g)/(r) t`
`0 = omega_(0) - (5)/(2) (mu g)/(r) (v_(0))/(mu g)`
`rArr" "omega_(0) = (5)/(2) (v_(0))/(r)`
Aliter : From conservation of angular momentum about the point of contact
`-I omega + mv_(0) r = 0`
`v_(0) = (2)/(5) (mr^(2)omega_(0))/(mr) = (2)/(5) r omega_(0)`
`omega_(0) = (5)/(2) (v_(0))/(r)`
Promotional Banner

Similar Questions

Explore conceptually related problems

A solid sphere of mass 10 kg is placed on a rough surface having coefficient of frictio mu=0.1A constant force F=7N is applied along a line passing through the centre of the sphere as shown in the figure. The value of frictional force on the sphere is

A uniform sphere of radius R is palced on a rough horizontal surface and given a linear velocity v_(0) and an angular velocity omega _(0) as shown . If the angular velocity and the linear velocity both become zero simultaneously, then

A ring of mass m and radius R is placed on a rough horizontal surface (co-efficient of friction mu ) with velocity of C.M. v_(0) and angular speed (2V_(0))/(R ) as shown in figure. Initially the ring is rolling with slipping but attains pure rolling motion after some time t . Then

A uniform circular disc of radius r is placed on a rough horizontal surface and given a linear velocity v_(0) and angular velocity omega_(0) as shown. The disc comes to rest after moving some distance to the right. It follows that

A wheel is released on a rough horizontal floor after imparting it an initial horizontal velocity v_(0) and angular velocity omega_(0) as shown in the figure below. Point O is the centre of mass of the wheel and point P is its instantaneous point of contact with the groundl. The radius of wheel is r and its radius of gyration about O is k . Coefficient of friction between wheel and ground is mu . A is a fixed point on the ground. If the wheel comes to permanent rest after sometimes, then :

A uniform circular disc placed on a horizontal rough surface has initially a velocity v_(0) and an angular velocity omega_(0) as shown in the figure. The disc comes to rest after moving some distance in the direction of motion. Then v_(0)//r omega_(0) is :

A uniform circular disc placed on a horizontal rough surface has initially a velocity v_(0) and an angular velocity omega_(0) as shown in the figure. The disc comes to rest after moving some distance in the direction of motion. Then v_(0)//omega_(0) is :

A sphere of mass M and radius R is moving on a rough fixed surface, having coefficient of friction mu . as shown in Fig. It will attain a minimum linear velocity after time ( v_(0)gtomega_(0)R)

a uniform circular disc of radiu8s r placed on a roughn horizontal plane has initial velocity v_(0) and an angul,ar velocity omega_(0) has shown The disc comes to rest after moving some distance in the direction of motion. Then

A solid sphere of mass m is lying at rest on a rough horizontal surface. The coefficient of friction between the ground and sphere is mu . The maximum value of F , so that the sphere will not slip, is equal to