Question

T = 2pi √m/g Check whether the equation is dimension ally correct. T→ Time period of a simple pendulum, m→ mass of the bob, g→ acceleration due to gravity​

Answer 1

Explanation:

Let Time period =T

Mass of the bob = m

Acceleration due to gravity = g

Length of string = L

Let

→ a=0 → Time period of oscillation is independent of mass of the bob

-2b=1

⇒b=_

b+c= 0

1/2 + c =0

c=1

Giving values to a,b and c in first equation T proportional m * g^-1/2 L^1/2 T proportional to root L/g

The real expression for Time period is

= 2 Pie root L/g

Therefore time period of oscillation depends only on gravity and length of the string.

Not on mass of the bob.