The period (T) of a simple pendulum is measured for different length (L), then graph of Log T against log L is

Options

A. a parabola
B. a circle
C. a straight line with a slope `(1)/(2)`
D. a straight line with a slope 2

Answer

C

Explanation

`T^(2)=4pi^(2)(L)/(g)`
`therefore 2 log T= log L+log (4pi^(2))/(g)`
`therefore log T=(1)/(2) log L +(1)/(2) log (4pi^(2))/(g)`
This is of the form y=mx+c
`therefore` It is straight line with a slope `(1)/(2)`