Using a simple pendulum experiment g is determind by measuring its time period T . Which of the following plots represent the correct relation between the pendulum length L and time period T ?

Step-by-step solution

The time period T of a simple pendulum of length L is given by the formula: T = 2 L g Squaring both sides, we get: T^2 = 4 ^2 L g Rearranging the equation to find the relationship between 1 T^2 and L : 1 T^2 = g 4 ^2 L Let y = 1 T^2 and x = L . The equation becomes: y = k x where k = g 4 ^2 is a constant. This is the equation of a rectangular hyperbola in the first quadrant. As L increases, 1 T^2 decreases non-linearly, approaching the axes asymptotically. Comparing this with the given plots, option (2) correctly r