Question

A cage revolves around a vertical circle of radius $R$ with constant linear speed $\sqrt{gR}$. 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 of the weight of the boy
• 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 of the weight of the boy

At highest point the velocity $v=\sqrt{gR}$
and Radial acceleration , $a_r=\frac{v^2}{R}=g$
Therefore, the weight machine will not record the weight of the boy.
At lowest point, the boy has resultant force equal to mg acting upward, so the normal reaction will balance the weight of boy mg and also provide the net upward force.Now the machine will record double weight of boy.
Ans:(A)