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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??
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 .......
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