The time period T of a simple pendulum of length L is measured. A graph is plotted with (T) on the y-axis and (L) on the x-axis. The shape of the resulting graph and its slope will be:

Step-by-step solution

The formula for the time period of a simple pendulum is: T = 2 L g Taking the natural logarithm on both sides gives: (T) = (2 L g ) Using the properties of logarithms: (T) = ( 2 g ) + (L^ 1/2 ) (T) = 1 2 (L) + ( 2 g ) This equation is of the linear form y = mx + c , where y = (T) and x = (L) . The slope m is 1 2 and the y-intercept is ( 2 g ) . Thus, the graph is a straight line with a slope of 1 2 . Answer: A straight line with slope 1 2