A uniform sphere of mass M and radius R is placed on a rough horizontal surface (Figure). The sphere is struck horizontally at a height h from the floor.
Match the Column I with Column II.
Column I | Column II | ||
(A) | (p) | Sphere rolls without slipping with a constant velocity and no loss of energy. | |
(B) | h = R | (q) | Sphere spins clockwise, loses energy by friction |
(C) | (r) | Sphere spins anti – clockwise loses energy by friction. | |
(D) | (s) | Sphere hasonlya translational motion. Loses energy byfriction. |
Text Solution
Verified by ExpertsA
: Let the sphere of mass M and radius R be struck horizontally at a height h from the floor, as shown in the figure.
The sphere will roll without slipping when 
angular momentum of sphere about its centre of mass is. 
( 
For a sphere , 
)
or 
The sphere will roll without slipping with a constant velocity and no loss energy when, 
Torque due to applied force about centre of mass, 
If, 
sphere will have only translational motion. It would lose energy by friction.
The sphere will spin clockwise, when 
is positive, i.e., h > R
Again the sphere will spin anticlockwise, when 
is negative, i.e, , h < R
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