Home
Class 11
PHYSICS
A uniform sphere of mass m and radius R ...

A uniform sphere of mass `m` and radius `R` is placed on a rough horizontal surface. The spher is struck horizontally at a height h from the floor. Show that the sphere rolls without slipping with a constant velocity, when `h = 7R//5`.

Text Solution

Verified by Experts

The sphere will roll without slipping with constant velocity when `omega = (v)/(R )`
Now, angular momentum of sphere about c.m Fig.
`mv(h - R) = I omega = ((2)/(5)m R^(2))((v)/(R ))`
`mv(h - R) = (2)/(5)mvR`
`h - R = (2)/(5)R`
`h = (2)/(5)R + R = (7)/(5)R`
Promotional Banner

Topper's Solved these Questions

  • SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

    PRADEEP|Exercise VALUE BASED QUESTIONS|5 Videos

  • SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

    PRADEEP|Exercise CURIOSITY QUESTIONS|4 Videos

  • SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

    PRADEEP|Exercise ADDITIONAL EXERCISES|11 Videos

  • RAY OPTICS

    PRADEEP|Exercise Problem For Practice(a)|25 Videos

  • THERMODYNAMICS

    PRADEEP|Exercise Assertion- Reason Type Questions|19 Videos

Similar Questions

Explore conceptually related problems

A uniform sphere of mass m and radius R is placed on a rough horizontal surface [Fig.] The sphere is struck horizontally at a hight h from the floor. Match the following : (a) h = R//2 (i) Sphere rolls without slipping with a constant velocity and no loss of energy. (b) h = R (ii) Sphere spins clockwise, loses energy by friction. (c ) h = 3R//2 (iii) Sphere spins anti-clockwise, loses energy by friction. (d) h = 7R//5 (iv) Sphere has only a translational motion, looses energy by friction.

A solid sphere of mass ma nd radis R is placed on a rough horizontal surface A horizontal force F is applied to sphere at a height h, (0lehleR) from centre. If sphere rolls slipping then,

A solid sphere of mass M and radius R is placed on a rough horizontal surface. It is stuck by a horizontal cue stick at a height h above the surface. The value of h so that the sphere performs pure rolling motion immediately after it has been stuck is

A bullet of mass m is fired horizontally into a large sphere of mass M and radius R resting on a smooth horizontal table. The bullet hits the sphere at a height h from the table and sticks to its surface. If the sphere starts rolling without slippng immediately on impact, then

A uniform solid cylinder of mass m and radius R is placed on a rough horizontal surface. A horizontal constant force F is applied at the top point P of the cylinder so that it start pure rolling. The acceleration of the cylinder is