Question

A stone is kept hanging from the end of a round table of
radius 22.6 cm by means of a thread. The table is
rotated such that the thread makes an angle of 30°
with the vertical. What is the angular velocity of the
table?​

Answer 1

Answer:

the string is vertical at  the lowest postion

Explanation:

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Answer 2

Explanation:

Given A stone is kept hanging from the end of a round table of radius 22.6 cm by means of a thread. The table is  rotated such that the thread makes an angle of 30°  with the vertical. What is the angular velocity of the  table?

• Let ω be the angular velocity and m be the mass of stone.
• There are three forces acting on the stone in equilibrium position. One is weight acting vertically downwards, tension in the string and the centrifugal force acting horizontally.
• The angle opposite to mg is 120 degree and that opposite to m ω^2 r is 150 degree.
• Applying Lami’s theorem we get
•                      So m ω^2 r / sin 150 = mg / sin 120
•                      So m ω^2 r / sin 30 = mg / sin 60
•                     So r ω^2 = g / √3
•                     Or ω = √g / √3
•       Rationalizing the denominator we get
•                 So ω = √g / √3 r x √3 r / √3r
•                           = √ (√3 g / 3 r)

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