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 ∝
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
So,
Regards
Let ∝
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
So,
Regards