A system consists of two identical spheres each of mass 1 . 5kg and...

A system consists of two identical spheres each of mass

1 . 5kg

and radius

50cm

at the ends of a light rod. The distance between the centres of the two spheres is

5m .

What will be the moment of inertia of the system about an axis perpendicular to the rod passing through its midpoint? A system consists of two identical spheres each of mass 1 . 5kg and radius 50cm at the ends of a light rod. The

A system consists of two identical spheres each of mass 1 . 5kg and radius 50cm at the ends of a light rod. The

Options

A $1 . 905 \times {10}^{5}kg{m}^{2}$
B $18 . 75kg{m}^{2}$
C $19 . 05kg{m}^{2}$
D $1 . 875 \times {10}^{5}kg{m}^{2}$

Correct answer

C. $19 . 05kg{m}^{2}$

Step-by-step solution

\leftI = \left(\dfrac{2}{5}M{R}^{2} + M{x}^{2}\right) \times 2 = \left[\dfrac{2}{5} \times 1 . 5 \times {\left(0 . 5\right)}^{2} + 1 . 5 \times {\left(2 . 5\right)}^{2}\right)] \times 2 = [ 0 . 15 + 9 . 375 ] \times 2 = 19 . 05{kgm}^{2}

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