When a particle of mass m is suspended from a massless spring of natural length $l$ , the length of the spring becomes 21 . When the same mass moves in conical pendulum as shown in figure, the length of the spring becomes L . The radius of the circle of conical pendulum is:

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mg = k 1 ​ k ( L − l ) 1 − L 2 R 2 ​ ​ = k l ( 2 ) ​ 1 − L 2 R 2 ​ = ( L − l ) 2 l 2 ​ ​ { ( L − l ) 2 ( L − l ) 2 − l 2 ​ } L 2 = R 2 ​ ​ r = ( ( L − l ) L ​ ) ( L 2 − 2 L l )

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JEE Advanced (2028)