question_answer

The moment of inertia of a uniform cylinder of length\[\ell \]and radius R about its perpendicular bisector is I. What is the ratio \[\ell /R\]such that the moment of inertia is minimum?                                                          [JEE Main 2017]

A)   1                               

B)   \[\frac{3}{\sqrt{2}}\]

C)   \[\sqrt{\frac{3}{\sqrt{2}}}\]     

D)        \[\frac{\sqrt{3}}{2}\]

Correct Answer: C

Solution :

[c]

or                               ..

Also

Put in equation

For maxima & minima

Or