question_answer

    A sphere of mass 0.20 kg is attached to an inextensible string of length 0.5m 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                               

B)  2.5 m/s

C)  3.2 m/s               

D)  4.7 m/s

Correct Answer: A

Solution :

                As shown in figure                 \[T\sin \theta =\frac{m{{v}^{2}}}{r}\]                 \[T\cos \theta =mg\] So, \[\tan \theta =\frac{{{v}^{2}}}{rg}=\frac{r}{\sqrt{{{l}^{2}}-{{r}^{2}}}}\] \[\therefore \]  \[v={{\left[ \frac{{{r}^{2}}g}{{{({{l}^{2}}-{{r}^{2}})}^{1/2}}} \right]}^{1/2}}\]                 \[={{\left[ \frac{0.09\times 10}{{{(0.25-0.09)}^{1/2}}} \right]}^{1/2}}=1.5\,m/s\]