Question #38919

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A particle of mass M is attached to the end of a light inextensible string and hangs at rest with the upper end of the string attached to a point on the upper half of a fixed horizontal circular cylinder of radius R. The straight part of the string is of length πR and is vertical tangent to the cylinder.The particle is projected horizontally with velocity V at right angles to the axis of the cylinder so that string wrap round the cylinder.

1)Find the tension in the string when the length of the straight part is Rθ

2)Show that if the string becomes slack when θ=α , then α≥β,where βis the acute angle given by cotβ=3β

A particle of mass M is attached to the end of a light inextensible string and hangs at rest with the upper end of the string attached to a point on the upper half of a fixed horizontal circular cylinder of radius R. The straight part of the string is of length πR and is vertical tangent to the cylinder.The particle is projected horizontally with velocity V at right angles to the axis of the cylinder so that string wrap round the cylinder.

1)Find the tension in the string when the length of the straight part is Rθ

2)Show that if the string becomes slack when θ=α , then α≥β,where βis the acute angle given by cotβ=3β

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