A heavy small sized sphere is suspended by a string of length 𝑙. The sphere is rotated uniformly in a horizontal circle with the string making an angle θ with the vertical. The time period of this conical pendulum is

Question : A heavy small sized sphere is suspended by a string of length 𝑙. The sphere is rotated uniformly in a horizontal circle with the string making an angle θ with the vertical. The time period of this conical pendulum is

(A) 2\pi \sqrt{\dfrac{2\tan \theta }{g}}

(B) 2\pi \sqrt{\dfrac{2\sin \theta }{g}}

(C) 2\pi \sqrt{\dfrac{l}{g}}

(D) 2\pi \sqrt{\dfrac{2\cos \theta }{g}}

Answer : option (D)

Solution :

A heavy small sized sphere is suspended by a string of length 𝑙. The sphere is rotated uniformly in a horizontal circle with the string making an angle θ with the vertical. The time period of this conical pendulum is
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