Home
Class 11
PHYSICS
A uniform ball of radius r rolls without...

A uniform ball of radius `r` rolls without slipping down from the top of a sphere of radius `R` Find the angular velocity of the ball at the moment it breaks off the sphere. The initial velocity of the ball is negligible.

A

`sqrt((5g(R+r))(17r^(2)))`

B

`sqrt((10g(R+r))/(17r^(2)))`

C

`sqrt((5g(R-r))/(10r^(2)))`

D

`sqrt((10g(R+r))/(7r^(2)))`

Text Solution

Verified by Experts

The correct Answer is:
B
`(mv^(2))/((R+r))=mgcostheta`
`mgh=l1/2mv^(2)+1/2Iomega^(2)`

`mg(R+r)(1-costheta)=1/2mv^(2)+1/5mv^(2)`
`=7/10mv^(2)`
`10/7mg(R+r)(1-costheta)=mgcostheta`
`mv^(2)=10/7mg(R+r)(1-costheta)`
`10/7=17/7costheta or costheta=10/7`
`v=sqrt(g(R+r)costheta)=sqrt(10/7g(R+r))`
and `omega=v/r=sqrt((10g(R+r))/(17r^(2)))`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • RIGID BODY DYNAMICS 2

    CENGAGE PHYSICS|Exercise Multiple Correct|26 Videos

  • RIGID BODY DYNAMICS 2

    CENGAGE PHYSICS|Exercise Linked Comprehension|71 Videos

  • RIGID BODY DYNAMICS 2

    CENGAGE PHYSICS|Exercise Subjective|19 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 sphere of radius R/16 starts rolling down without slipping from the top of another sphere of radius R=1m . The angular velocity of the sphere of in rad s^(-1) , after it leaves the surface of the larger sphere is 8 xn . Where n =--

A small body A starts sliding off the top of a smooth sphere of radius R. Find the angle theta (figure) corresponding to the point at which the body breaks off the sphere, as well as the break-off velocity of the body.

Knowledge Check

  • A uniform ball of radius R rolls without slipping between the rails such that the horizontal distance is sqrt(3)R between the two contact points of te rails of the ball. Figure (a) shows front view of the ball and figure (b) shows the side view of the ball. v_(CM) is the velocity of centre of mass of the ball and omega is the angular velocity of the ball after rolling down a distance 2h along the incline then

    A
    `V_(CM)=omegaR`
    B
    `V_(CM)=omega R/2`
    C
    `V_(CM)=sqrt((10gh)/13)`
    D
    `V_(CM)=sqrt((10 gh)/7)`

  • A small solid sphere of radius r rolls down an incline without slipping which ends into a vertical loop of radius R . Find the height above the base so that it just loops the loop

    A
    `5/2R`
    B
    `5/2(R-r)`
    C
    `25/10(R-r)`
    D
    `27/10R-(17r)/10`

  • A solid sphere of radius 'r' is rolling with velocity V on a smooth plane. The total kinetic energy of sphere is

    A
    `7/10 mv^(2)`
    B
    `3/4 mv^(2)`
    C
    `1/2 mv^(2)`
    D
    `1/4 mv^(2)`

    • Similar Questions

    Explore conceptually related problems

    A uniform ball of radius r is placed on the top of a sphere of radius R = 10 r. It is given a slight push due to which it starts rolling down the sphere without slipping. The spin angular velocity of the ball when it breaks off from the sphere is omega=sqrt((p)/(q)((g)/(r))) , where g is the acceleration due to gravity and p and q are the smallest integers. What is the value of p+q ?

    A sphere of radius R rolls without slipping between two planks as shown in figure. Find (a) Speed of centre of sphere (b) Angular velocity of the sphere

    A spherical ball of mass m and radius r rolls without slipping on a rough concave surface of large radius R. It makes small oscillations about the lowest point. Find the time period.

    A uniform sphere of mass m and radius R starts rolling without slipping down an inclined plane at an angle alpha to the horizontal. Find the time dependence of the angular momentum of the sphere relative to the point of contact at the initial moment. How will the obtained result change in the case of a perfectly smooth inclined plane?

    the disc of the radius r is confined to roll without slipping at A and B if the plates have the velocities shown, determine the angular velocity of the disc.

    Home
    Profile