Question

Three identical particles are joined together by a thread in the way such that A is l meters away from point O, B 2l meters away and C 3l meters away. All the three particles are moving on a smooth horizontal plane about point O. If the speed of the outermost particle is v then find the ratio of tension in the three sections of the thread.

Answer 1

Answer on Question #55907-Physics-Classical Mechanics

Three identical particles are joined together by a thread as shown in the figure. All the three particles are moving on a smooth surface horizontal plane about point O. If the speed of the outermost particle is V, then the ratio of tensions in the three sections of the string is: (Assume that the string remains straight)

(1)3:5:7

(2)3:4:7

(3)7:11:6

(4)3:5:6

(Hint: the distance between each point is l)

Solution

Let the angular speed of the thread is $\omega$ .

For particle C

$$T _ {3} = m \omega^ {2} 3 l.$$

For particle B

$$T _ {2} - T _ {3} = m \omega^ {2} 2 l \rightarrow T _ {2} = m \omega^ {2} 5 l.$$

For particle A

$$T _ {1} - T _ {2} = m \omega^ {2} l \rightarrow T _ {1} = m \omega^ {2} 6 l.$$

Answer: (4) 3:5:6.

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