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Grade: 11
        

4 A bead of mass m is located on a parabolic wire with its axis vertical and vertex directed towards downward as in figure and whose equation

is x² = ay. If the coefficient of friction is µ, the highest distance above
the x-axis at which the particle will be in equilibrium is

(a) µa (b) µ²a (c)1/4 µ^2 g (d)1/2µ^ g

one year ago

Answers : (1)

Vikas TU
6887 Points
							
tangent at any x distance would be => tanthetha =2x/a
Now
friction = umgcosthetha
Balancing friction with mg*sin(thetha) we get,
ucosthetha = sinthetha
or
tan(thetha) = u
2x/a = u
x = au/2
The highest point would be,
y = (au/2)^2/a => a^2u^2/4a => au^2/4 
one year ago
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