A car moves uniformly along a horizontal sine curve y=a sin (xα) , where a and α are certain constants. The coefficient of friction between the wheels and the road is equal to k. The maximum constant speed at which the car can travel without sliding is
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a
αkga
b
-αkga
c
kgαa
d
-kgαa
answer is A.
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Detailed Solution
The radius of curvature is f≤f2 or f≤kmg Or mv2R≤kmg or v2R≤kg∴vmax2Rmin=kg∴vmax=kgRminxa=π2∴Rmin=α2a ( from equ (i))vmax=kgα2a=αkga