Question

What is the slope of T² vs l graph of a pendulum. How can we measure value of g (acceleration due to gravity) using this slope?

Answer 1

T=2π √L/G, where G = acceleration due to gravity. From your second graph, find the value of G. There you plotted T 2 vs length. If we square the formula for the period, we obtain T 2 = 4π2 / g l.

Answer 2

The slope of the T² vs l graph of a pendulum gives the measured value of g (acceleration due to gravity).

• The time period T of a simple pendulum is given by the formula T = 2π √(l/g). Here l is the length of the pendulum.
• Squaring both the sides, we get T² = 4π² l/g

        Since 4π² and g are constants,

      ⇒  T² = ml

Here m is the slope of the  T² bs l graph. The value of the slope m =  4π²/g

• Taking the value of π² = 10 and replacing it in the above equation, we can calculate the value of g from the slope of the graph.
• g = 40/m