Two pendulums differ in lengths by `22m`. They oscillate at the same place so that one of then makes 30 oscillations and the other makes 36 oscillations during the same time. The length `(` in `cm)` of the pendulum are `:`

Options

A. 72 and 50
B. 60 and 38
C. 50 and 28
D. 80 and 58

Answer

A

Explanation

Time period of pendulum is
`T=2pisqrt((L)/(g)) therefore(T_(1))/(T_(2))=sqrt((L_(1))/(L_(2)))`
Also, `(T_(1))/(T_(2))=(N_(2))/(N_(1))` where `N_(1)=30 and N_(2)=36`
`therefore sqrt((L_(1))/(L_(2)))=(N_(2))/(N_(1))=(36)/(30)` . . . (i)
`L_(1)-L_(2)=22cm` . . . (ii)
Solving the eqs. (i) and (ii), we get
`L_(1)=72cm and L_(2)=50cm`