Question

A hollow vertical cylinder of radius r and height h has a smooth internal surface. A small particle is placed in contact with the inner side of the upper rim, at point A, and given a horizontal speed u, tangential to the rim. It leaves the lower rim at point B, vertically below A. If n is an integer then-

• A. $\frac{u}{2\pi r}\sqrt{2h/g}$ = n
• B. $\frac{h}{2\pi r}$ = n
• C. $\frac{2\pi r}{h}$ = n
• D. $\frac{u}{\sqrt{2gh}}$ = n

Answer 1

Answer: (A)

$\frac{u}{2\pi r}\sqrt{2h/g}$ = n

Answer 2

Time taken in falling = $\sqrt { \frac { 2 h } { g } }$

Distance moved in horizontal plane

= $u \cdot \sqrt { \frac { 2 h } { h } } = n .2 \pi r$