Question

A cage revolves around a vertical circle of radius R with constant linear speed √gR. The cage is connected to the revolving arm in such a manner that a boy of mass m remains always vertical while standing on a weighing machine kept inside the cage. It is found that

• A. The reading at lowermost point L is greater than the reading at highest point H by two times.
• B. The readings are same at all the points on the vertical circle.
• C. The reading at lowermost point L is less than the reading at highest point H by two third.
• D. The reading at lowermost point L is five times the reading at the highest point H.

Answer 1

Answer: (A)

The reading at lowermost point L is greater than the reading at highest point H by two times.

Answer 2

At highest point v = $\sqrt { \operatorname { Rg } }$ and radial acceleration,

a_r = $\frac { v ^ { 2 } } { R } = \frac { R g } { R } = g$

Thus, the weighing machine will not record the weight of the man.

At lowest point, the boy has a resultant force equal to mg acting upward so the normal reaction has to balance the weight of the boy mg and also to provide net upward force also. Hence, the machine will record double the weight of the boy.