At a particular place, a simple pendulum of length 1m, makes 400 oscillations in 13 minute. What is the length of a second's pendulum at this place ?

Options

A. 98 cm
B. 100 cm
C. 102 cm
D. 105 cm

Answer

D

Explanation

`T_(1)=(13xx60)/(400)=(39)/(20)s and T_(2)=2s`
`because T=2pi sqrt((l)/(g)) therefore (39)/(40)=2pi sqrt((l_(1))/(g))`
and `2=2pi sqrt((l_(2))/(g))`
g has the same value in both cases.
`therefore (2)/((39)/(20))=sqrt((l_(2))/(100))`
`((40)/(39))^(2)=(l_(2))/(100) therefore l_(2)=100xx1.05=105 cm`