Question

A hollow vertical drum of radius r and height H has a small particle in contact with smooth inner surface of the upper rim at point P. The particle is given a horizontal speed u tangential to the rim. It leaves the lower rim at Q vertically below P. Taking n as an integer for number of revolutions, we get

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

Answer 1

Answer: (D)

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

Answer 2

For vertical motion

H = $\frac{1}{2}gt^{2}$ or t = $\sqrt{\frac{2H}{g}}$

For horizontal motion, distance covered is given by,

2πn = ut

or 2πrn = $\sqrt{\frac{2H}{g}}$

or n = $\frac{u}{2\pi r}\sqrt{\frac{2H}{g}}$