Home
Class 11
PHYSICS
A uniform spherical shell of mass M and ...

A uniform spherical shell of mass `M` and radius `R` rotates, about a vertical axis on frictionless bearing. A massless cord passes around the equator of the shell., over a pulley of rotational inertia `I` and radius `r` and is attached to small object of mass `m` that is otherwise free to fall under the influence of gravity. There is no friction of pulley's axle, the cord does not slip on the pulley. What is the speed of the object after it has fallen a distance `h`. from rest? Use work-energy considerations.

Text Solution

Verified by Experts

Using conservation of energy principle, we have fall in `PE` of te block `=` Gain in `KE` of the block `+` Rotational `KE` of the pulley `+` Rotational `KE` of the shell.
or `mgh=1/2mv^(2)+1/2Iomega^(2)+1/2((2MR^(2))/3)omega^('2)`
where `omega=v/r` and `omega'=v/R`
After substituting these values in the above equation and solving we get
`v^(2)=(mgh)/((m/2+I/(2r^(2))+M/3))`
Promotional Banner

Topper's Solved these Questions

  • RIGID BODY DYNAMICS 2

    CENGAGE PHYSICS|Exercise Exercise 3.2|13 Videos

  • RIGID BODY DYNAMICS 2

    CENGAGE PHYSICS|Exercise Exercise 3.3|21 Videos

  • RIGID BODY DYNAMICS 2

    CENGAGE PHYSICS|Exercise Solved Examples|12 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 spherical shell of mass M = 4.5 kg and radius R = 8.5 cm can rotate about a vertical axis on frictionless bearings (Fig. 10-69). A massless cord passes around the equator of the shell, over a pulley of rotational inertia I=3.0xx10^(-3)kg*m^(2) and radius r = 5.0 cm, and is attached to a small object of mass m = 0.60 kg. There is no friction on the pulley's axle, the cord does not slip on the pulley. What is the speed of the object when it has fallen 82 cm after being released from rest? Use energy considerations.

A thin spherical shell of mass M and radius R has a small hole. A particle of mass m released at its mouth. Then

A uniform solid cylinder of mass M and of radius R rotates about a frictionless axle. Two masses are suspended from a rope wrapped arround the cylinder. If the system is released from rest, the tension in each rope is?

A uniform disc of mass M and radius R is mounted on an axle supported in frictionless bearings. A light cord is wrapped around the rim of the disc and a steady downward pull T is exerted on the cord. The angular acceleration of the disc is

Moment of inertia of a cylindrical shell of mass M, radius R and length L about its geometrical axis would be -

Consider a thin spherical shell of uniform density of mass M and radius R :

A small area is removed from a uniform spherical shell of mass M and radius R. Then the gravitatioinal field intensity near the hollow portion is

A uniform solid sphere of mass m and radius r is suspended symmetrically by a uniform thin spherical shell of radius 2r and mass m .

A solid uniform sphere of mass M and radius R can rotate about a fixed vertical axis. There is no frictional torque acting at the axis of rotation. A light string is wrapped around the equator of the sphere. The string has exactly 6 turns on the sphere. The string passes over a light pulley and carries a small mass m at its end (see figure). The string between the sphere and the pulley is always horizontal. The system is released from rest and the small mass falls down vertically. The string does not slip on the sphere till 5 turns get unwound. As soon as 5^(th) turn gets unwound completely, the friction between the sphere and the string vanishes all of a sudden. (a) Find the angular speed of the sphere as the string leaves it. (b) Find the change in acceleration of the small mass m after 5 turns get unwound from the sphere.

A uniform solid cylinder of mass m and radius 2R rests on a horizontal table. A string attached to it passes over a pulley (disc) of mass m and radius R that is mounted on a fricitonaless axle through its centre . A block of mass m is suspended from the free end of the spring . The string does not slip over the pulley surface and the cylinder rolls without slipping on the table. Force of friction acting on the cylinder is

Knowledge Check

  • A thin spherical shell of mass M and radius R has a small hole. A particle of mass m released at its mouth. Then

    A
    the particle will execute `S.H.M` inside the shell
    B
    the particle will oscillate inside the shell, but the oscillations are not simple harmonic
    C
    the particle will not oscillate, but the speed the particle will go on increasing
    D
    none ot these

  • A uniform solid cylinder of mass M and of radius R rotates about a frictionless axle. Two masses are suspended from a rope wrapped arround the cylinder. If the system is released from rest, the tension in each rope is?

    A
    `(Mmg)/(M+m)`
    B
    `(Mmg)/(M+2m)`
    C
    `(Mmg)/(M+3m)`
    D
    `(Mmg)/(M+4m)`

  • A uniform disc of mass M and radius R is mounted on an axle supported in frictionless bearings. A light cord is wrapped around the rim of the disc and a steady downward pull T is exerted on the cord. The angular acceleration of the disc is

    A
    `T/(MR)`
    B
    `(MR)/T`
    C
    `(2T)/MR`
    D
    `(MR)/(2T)`