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varsha rao Grade: 11
        

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??

6 years ago

Answers : (1)

vikas askiitian expert
510 Points
										

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 .......

6 years ago
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