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Answer 1 · 2017-02-27T10:55:41

The length is $= 1 m$ $=1m$

The period of a simple pendulum is

$T = 2 π \sqrt{\frac{L}{g}}$ $T=2pisqrt(L/g)$

Period $= T s$ $=Ts$

Length $= L (m)$ $=L (m)$

Therefore,

$\frac{L}{g} = \frac{T}{4 π^{2}}$ $L/g=T/(4pi^2)$

In the first case, we have

$L = \frac{T g}{4 π^{2}} = \frac{4^{2} \cdot 9.8}{4 π^{2}} = 4 m$ $L=(Tg)/(4pi^2)=(4^2*9.8)/(4pi^2)=4m$

In the second case,

$T = \frac{60}{30} = 2 s$ $T=60/30=2s$

So,

$L = \frac{4 \cdot 9.8}{4 π^{2}} = 1 m$ $L=(4*9.8)/(4pi^2)=1m$