question_answer

If a boy swings in a circle so the minimum and maximum height from ground is\[3\,\,m\]and\[6\,\,m\], then, its maximum velocity is:

A) \[5\sqrt{2}m/s\]                              

B)  \[2\sqrt{5}m/s\]

C)  \[3\sqrt{5}m/s\]                             

D)  \[5\sqrt{3}m/s\]

Correct Answer: D

Solution :

Key Idea: Maximum velocity at lowest point is \[\sqrt{5}\]times maximum velocity at highest point. Diameter \[AB\] of circle is\[3\,\,m\] Therefore, radius\[r=\frac{3}{2}m\] velocity at\[A(v)=\sqrt{5gr}\] Given,\[g=10\,\,m/{{s}^{2}},\,\,r=\frac{3}{2}m\] \[\therefore \]  \[v=\sqrt{5\times 10\times \frac{3}{2}}=5\sqrt{3}m/s\]