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Grade: 11
        

A particle is compelled to move inside smooth vertical tube as shown in fig. The minimum speed at lowest point so that it can complete full circle is

10 months ago

Answers : (1)

Devang
52 Points
							
Lets assume that point A , when partical is situated at lowest point in vertical tube and point B , when partical is situated at highest point in vertical tube.
when partical is ,on point A
mechanical energy = kinatic energy + potational energy
= ½ m va2  + 0   …............(1)                         (hight is 0)
normal force = weight force
N = mg                               …............(2)
when partical is ,on point B
normal force = centripetal force
N = mvb2 / R   put  value of n in this eq.
mg = mvb2 / R  
v= (gR)1/2                            …............(3)
mechanical energy = kinatic energy + potational energy
= ½ m vb2 + mg(2R)
= ½ m (gR) + 2mgR
= 5/2 (gR)            ….............(4)
from law of coservation of mechanical energy 
(1) & (4)
½ m va2 = 5/2 (gR)
va= 5gR
va  =  (5gR)1/2
hence a partical is complete full circle its minimum velocity is  (5gR)1/2

10 months ago
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