A ring of radius R having uniformly distributed charge Q is mounted on a rod suspended by two identical strings. The tension in strings in equilibrium is T 0 . Now a vertical magnetic field is switched on and the ring is rotated at constant angular velocity ω . Find the maximum ω with which the ring can be rotated if the strings can withstand a maximum tension of 
.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. In equilibrium, 2T 0 = mg
or T 0 = 
… (1)
Magnetic moment, M = iA = 
( π R 2 )
τ = MB sin 90° = 
Let T 1 and T 2 be the tensions in the two strings when magnetic field is switched on (T 1 > T 2 ).
For translational equilibrium of ring in vertical direction
T 1 + T 2 = mg … (2)
For rotational equilibrium,
(T 1 – T 2 ) 
= τ = 
or T 1 – T 2 = 
… (3)
Solving equations (2) and (3), we have
T 1 = 
+ 
As T 1 > T 2 and maximum values of T 1 can be 
, we have
= T 0 + 
∴ ω max = 
.
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