# 11. Suppose that period of oscillation of the simple pendulum depends on (i) mass of the bob (m) (ii) length L of the pendulum and (ii) acceleration due to gravity g at the plate. Derive expression for its time period, using method of dimensions.

Dear Student ,

Let  $t$

Where a, b and c are the powers of m (mass), l (length) and g (acceleration due to gravity)

or,    ..........(i)

Where k is dimensionless constant of proportionality.
Writing the dimensions in terms of M, L and T on each side of equation (i), we get

Applying the principal of homogeneity of dimensions, we get

Putting the value of c in equation (iii), we get

Now, putting the values of a, b and c in equation (i), we get

Using other methods, we calculate the value of $k=2\pi$

So, $t=2\pi \sqrt{\frac{l}{g}}$

Regards

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