Question

A small particle of mass ${}^{\prime }{m}^{\prime }$ starts sliding down from the top of a hemispherical bowl of radius ${}^{\prime }{r}^{\prime }$. The particle and the surface of the hemisphere are frictionless. The heigth from the ground at which the particle leaves contact with the sphere is:

• A. $\frac{2r}{3}$
• B. $\frac{3r}{2}$
• C. $\frac{r}{2}$
• D. $\frac{r}{3}$

Answer 1

The correct option is A $\frac{2r}{3}$

The particle after starting from point A reaches the point P where it leaves contact with the surface.

For the particle to loose contact at P, $cos\theta =\frac{2}{3}$

$\therefore$ Height from the ground $OB=rcos\theta =\frac{2r}{3}$