Question

A small sized mass m is attached by a massless string (of length L) to the top of a fixed frictionless solid cone whose axis is vertical. The half angle at the vertex of the cone is . If the mass m moves around in a horizontal circle at speed v, what is the maximum value of v for which mass stays in contact with the cone ? (g is acceleration due to gravity.)

Answer 1

Correct option (c) \(\sqrt{gL\sin\theta.\tan\theta}\)

Explanation:

\(T \sin\theta = \frac{mv^2}R\)  ......(1)

\(T\cos \theta = mg\)  ......(2)

Solving equation (1) and (2)

\(\frac{mg}{\cos\theta} \sin\theta = \frac{{m\,v_{max}}^2}{Lsin\theta}\)

\({v_{max}}^2 = L\sin\theta\tan\theta\)

\(v_{max} = \sqrt{L\sin\theta\tan\theta}\)

Answer 2

Correct option-

 

Explanation:-

At maximum velocity the mass will just loose contact with cone and will behave like free conical pendulum with time period