l - T and `l-T^(2)` graphs of a simple pendulum on earth are as shown in the figure. The x-coordiante (OA) of point of intersection of the graphs is nearly equal to (on the earth `g = 9.8ms^(-2)`)

Options

A. 20 cm
B. 25 cm
C. 50 cm
D. 100 cm

Answer

B

Explanation

Slope of `l=T^(2)` graph = `(T^(2))/(l)`
But, `g=4pi^(2)(l)/(T^(2))`
`therefore (T^(2))/(l)=(4pi^(2))/(g)`
`T=T^(2)=1s` at the point of intersection
`therefore (1)/(l)=(4pi^(2))/(g),l=(g)/(4pi^(2))~~(1)/(4)m=25cm`