Question

A machine, in an amusement park.consists of a cage at the end of one arm, hinged at o The cage revolves along a vertical circle of radius r (ABCDEFGH) about its hinge O. at constant linear speed vor The cage is so attached that the man of weight w standing on a weighing machine, inside the cage, is always vertical. Then which of the following is correct: E O co (A) the reading of his weight on the machine is the same at all positions (B) the weight reading at Ais greater than the weight reading at E by 2 w (C) the weight reading at Gow (D) the ratio of the weight reading at E to that at A = 0 (E) the ratio of the weight reading at A to that at C = 2​

Answer 1

Answer:

A machine in an amusement part consists of a cage at the end of one arm hinged at O The cage revolves along a vertical circle of radius r(ABCDFGH) about its hinged O, at constant linear speed. v=gr The cage is so attached that the man of weight ′w′ standing on a weighing machine inside the cage is always vertical.

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Answer 2

Answer:

The correct option is E) The ratio of the weight reading at A to C is 2.

Explanation:

• At A, the man is at the lowermost point of the circle
• Both the centripetal force and gravitational force acting on the man at A act downwards
• So the weight is the sum of the centripetal force and the gravitational force
• Weight at A = mv²/R + mg
• v = √gR
• Weight at A = mg + mg = 2 mg
• At point C, the man is halfway to the top, the centripetal force acts horizontally, so it cannot be used to calculate the weight
• The only vertical force acting on the man at C is the gravitational force
• Weight at C = mg
• Weight reading A/Weight reading C = 2mg/ mg = 2

Therefore, the correct option is E.

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