Question

When the length of a simple pendulum is increased by $36cm$, its time period of oscillation is found to increase by $25$%. The initial length of the simple pendulum is (Acceleration due to gravity $=9.8{ms}^{-2}$) :

• A. $36cm$
• B. $25cm$
• C. $64cm$
• D. $46cm$

Answer 1

The correct option is C $64cm$

$T=2\pi \sqrt{\frac{l}{g}}1.25T=2\pi \sqrt{\frac{l+36}{g}}\Rightarrow 1.25=\sqrt{\frac{l+36}{l}}\Rightarrow 1.5625l=l+36\Rightarrow l=\frac{36}{.5625}=64cm$