Check the correctness of the equation dimensionally t = 2gl . Where t is the time period,‘l’ is effective length and ‘g’ is acceleration due to gravity.

To check the correctness of the equation dimensionally, we need to compare the dimensions of both sides of the equation.

Let's start by analyzing the dimensions of each variable in the equation:

• The time period, 't', is measured in seconds (s).
• The effective length, 'l', is measured in meters (m).
• The acceleration due to gravity, 'g', is measured in meters per second squared (m/s^2).

Now, let's analyze the dimensions of the right-hand side of the equation, 2πgl:

• The constant 2π is dimensionless.
• The acceleration due to gravity, 'g', is measured in meters per second squared (m/s^2).
• The effective length, 'l', is measured in meters (m).

Multiplying these dimensions together, we get:

2πgl = (dimensionless) * (m/s^2) * (m) = m^2/s^2

Comparing the dimensions of the left-hand side (t) and the right-hand side (2πgl), we see that they have the same dimensions (m^2/s^2). Therefore, the equation is dimensionally correct.