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physics

mechanics

Easy

Question

Moment of inertia of a rod of mass M and length L about an axis passing through a point midway between centre and end is

$\frac{7 M L^{2}}{48}$
$\frac{M L^{2}}{12}$
$\frac{M L^{2}}{6}$
$\frac{7 M L^{2}}{24}$

The correct answer is: $\frac{7 M L^{2}}{48}$

From theorem of parallel axes,
$I equals I subscript CM plus M x squared equals fraction numerator M L squared over denominator 12 end fraction plus M open square brackets L over 4 close square brackets squared equals fraction numerator M L squared over denominator 12 end fraction plus fraction numerator M L squared over denominator 16 end fraction equals fraction numerator 7 M L squared over denominator 48 end fraction$

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