A particles of mass m is attached at one end of a light, inextensible string of length 𝓁 whose other end is fixed at the point C. At the lowest point the particle is given minimum velocity to complete the circular path in the vertical plane. As it moves in the circular path the tension in the string changes with 
. 
is defined in the figure. As 
varies from ‘0’ to ‘2 
’ (i.e. the particle completes one revolution) plot the variation of tension ‘T’ against ‘ 
’.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. By Newton ’ s law at B
T – mg cos θ = 
By energy conservation b/w A and B
mg λ (1 – cos θ ) + 
mv 2 = 
m (5 λ g)
mv 2 = m 5 λ g – 2mg λ (1 – cos θ )
T = mg cos θ + m 5 g – 2mg (1 – cos θ )
= 3 mg + 3 mg cos θ
= 3mg (1 + cos θ ) = 6 mg cos 2 ( θ /2)
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