Looking into the fig.

Given in the question that a perpendicular line passes through 50th particle.

moment of inertia along BC

Where,

m=mass of the particle

r=distance or radius

Now let us consider those two particles at position 49 cm and 51 cm.

Moment inertial due to these two particles will be

This value up to 50 becomes –

Therefore, total moment of inertia

Using Arithmetic Progression, the equation for sum of square of n natural numbers is given by

Solving for moment of Inertia, with = 50, we will get-