A small sphere of mass m suspended by a thread is first taken aside so that the thread forms the right angle with the vertical and then released, then:
(i) Find the total acceleration of the sphere and the thread tension as a function of 
, (the angle of
deflection of the thread from the vertical)
(ii) Find the angle 
between the thread and the vertical at the moment when the total acceleration vector
of the sphere is directed horizontally
(iii) Find the thread tension at the moment when the vertical component of the sphere ’ s velocity
is maximum
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i)
at θ angle θ a t = g sin θ
from centripetal acceleration
T – mg cos θ = 
...(1)
From energy conservation :
0 + mg λ cos θ = 
mv 2
⇒ v = 
....(2)
from (1) & (2)
T = 3mg cos θ
a C = 2g cos θ
a = 
= g 
(ii) Vertical component of sphere velocity is maximum when acceleration in vertical is zero that means net force in vertical direction is zero.
Net force in vertical at θ angle
T cos θ = mg
T = 
...(3)
and tension also from equation T = 3mg cos θ ....(4)
from (3) & (4)
3 mg cos θ = 
⇒ cos θ = 
T = mg 
Ans.
(iii) Total acceleration is directed along horizontal that means a vertical = 0
cos θ = 
Ans.
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