Question

Water in a bucket is whirled in a vertical circle with string attached to it. The water does no fall down even when the bucket is inverted at the top of its path. We conclude that in this position
(a) $mg=\frac{m{v}^2}{r}$
(b) mg is greater than $\frac{m{v}^2}{r}$
(c) mg is not greater than $\frac{m{v}^2}{r}$
(d) mg is not less than $\frac{m{v}^2}{r}$.

Answer 1

(c) mg is not greater than $\frac{m{v}^2}{r}$

At the top of the path, the direction of mg is vertically downward and for centrifugal force $\left(\frac{m{v}^2}{r}\right)$, the direction is vertically upward. If the vertically downward force is not greater, water will not fall.