A heavy particle of weight W , attached to a fixed point by a light inextensible string , describes a circle in a vertical plane. The tension in the string has values mW and nW respectively when the particle is at the highest and the lowest points of its path . Show that n = m + 6.
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Step-by-step explanation:
v°= velocity at lowest point.
Tb= tension at bottom = mw
Tt= tension at top = nw
=> mw + w = mv^2/r ------ 1
=> nw - w = mv°^2/r ------ 2
according to law of conservation of mass
=> v°^2 - v^2 = 4gr ...-------3
subtracting equation 1 from equation 2 we get ,
=> m(v°^2 - v^2) / r = nw - mw -2w ...
from 3
=> 4mg = (n-m)w - 2 mg ( since w = mg )
=> 6w = (n-m)w
=> n-m = 6
=> n=6+m
HENCE PROOVED
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