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A solid sphere has combined linear and r...

A solid sphere has combined linear and rotation motion as shown in figure. The velocity of its centre of mass when it starts pure rolling is (R = radius of sphere)

A

`6v_0 /7`

B

`v_0/7`

C

`5v_0 /6`

D

`v_0 /2`

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(i) A solid sphere of radius R is released on a rough horizontal surface with its top point having thrice the velocity of its bottom point A (V_(A) = V_(0)) as shown in figure. Calculate the linear velocity of the centre of the sphere when it starts pure rolling. (ii) Solid sphere of radius R is placed on a rough horizontal surface with its centre having velocity V_(0) towards right and its angular velocity being omega_(0) (in anticlockwise sense). Find the required relationship between V_(0) and omega_(0) so that - (a) the slipping ceases before the sphere loses all its linear momentum. (b) the sphere comes to a permanent rest after some time. (c) the velocity of centre becomes zero before the spinning ceases.

A solid sphere is thrown on a horizontal rough surface with initial velocity of centre of mass V_0 without rolling. Velocity of its centre of mass when its starts pure rolling is

Knowledge Check

  • A hemispherical cavity of radius R is created in a solid sphere of radius 2R as shown in the figure . Then y -coordinate of the centre of mass of the remaining sphere is

    A
    `Y_("CM")=-R/15`
    B
    `Y_("CM")=-R/40`
    C
    `Y_("CM")=-R/30`
    D
    `Y_("CM")=-R/20`

  • Four solid spheres are made to move on a rough horizontal surface. Sphere P is given a spin and released. Sphere Q is given a forward linear velocity. Spheres R and S are given linear and rotational motions as shown in the figure. Directions of the friction force on spheres P,Q,R,S are respectively. .

    A
    Right, Left, Right, Left
    B
    Right, Left, Left, Right
    C
    Left, Right,Left, either Left or Right
    D
    Right, Left,Left,either Left or Right

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