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प्रश्न
A body of mass ‘m’ performs uniform circular motion along a circular path of radius ‘r’ with velocity ‘v’. If its angular momentum is L, then the centripetal force acting on it is :
पर्याय
`("mL"^2)/"r"^3`
`"L"^2/("mr")`
`"L"^2/("mr"^2)`
`"L"^2/("mr"^3)`
उत्तर
`f_c = L^2/(mr^3)`
Lets consider,
m = mass of body performing circular motion
L = angular momentum
r = radius of circular path
v = velocity of the particle
L = mvr
The centripetal force,
`f_c = (mv^2)/r` ....(2)
Substitute equation (1) in equation (2), we get
`f_c = m/r ( L /(mr) )^2`
`f_c = L^2/(mr^3)`
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