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# a sphere of mass m is at rest on a rough horizontal surface. The coefficient of friction between the ground and sphere is u. then, max value of F so that the sphere will not slip is??

509 Points
10 years ago

let  a force F is applied at a distance r from the center ...

friction force will be in foreward direction

for translational motion

F - f =ma ..........1

for rotational motion

Fr  - fR = I(alfa) ..........2                               (R is radius of sphere)

for no slipping a = (alfa)R & Isphere = 2mR2/5

Fr - fR = 2maR/5 .................3

from 1 & 3

f = F(5r - 2R)/3R ......4

for rolling ,

f < or = umg

F(5r-2R)/3R = umg

F= 3umgR/(5r-2R)

this value of force is maximum .......