Q. A sphere of mass 0.2 kg is attached to an inextensible string of length 0.5 m whose upper end is fixed to the ceiling. The sphere is made to describe a horizontal circle of radius 0.3 m. The speed of the sphere will be
A) $1.5\ m\ s^{- 1}$
B) 2.5 $m\ s^{- 1}$
C) 3.2 $m\ s^{- 1}$
D) 4.7 $m\ s^{- 1}$
Explanation
(a) In figure, $T\sin{\theta = \frac{mv^{2}}{r}};Tcos\ \theta = mg;$
[image:4_image144.emf]
So, tan $\theta = \frac{v^{2}}{rg} = \frac{r}{\sqrt{l^{2} - r^{2}}}$
$v = \left\lbrack \frac{r^{2}g}{\left( l^{2} - r^{2} \right)^{1/2}} \right\rbrack^{1/2} = \left\lbrack \frac{0.09 \times 10}{(0.25 - 0.09)^{1/2}} \right\rbrack^{1/2}$
$= 1.5\ ms^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.