Question

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 $r\left(ABCDFGH\right)$ about its hinged $O$, at constant linear speed
$v=\sqrt{gr}$ The cage is so attached that the man of weight ${}^{\prime }{w}^{\prime }$
standing on a weighing machine inside the cage is always vertical.
Then which of the following is correct.

• A. the ratio of the weight reading at $A$ to that at $C=2$.
• B. the weight reading at $A$ is greater than the weight reading at $E$ by $2w$.
• C. the weight reading at $G$ is equal to $w$.
• D. the ratio of the weight reading at $E$ to that at $A=0$.

Answer 1

The correct option is A the ratio of the weight reading at $A$ to that at $C=2$.

$w=mg$

$\frac{m{v}^2}{r}=\frac{mgr}{r}=mg$

$\frac{weightofreadingatA}{weightofreadingatB}=\frac{2mg}{mg}=2$