Question #47b8a

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Answer 1 · 2017-12-26T16:22:26

See the explanation below

The length of the pendulum is $=l$

The period of the pendulum is $=T$

The period of a simple pendulum is

$T=2pisqrt(l/g)$

Taking natural logarithms on both sides

$lnT=ln(2pi)+1/2ln(l)-1/2ln(g)$

Differentiating the equation

$(DeltaT)/T=0+1/2(Deltal)/l-1/2(Deltag)/g$

You cannot substract errors

Therefore,

$|(DeltaT)/T|=1/2|(Deltal)/l|+1/2|(Deltag)/g|$

The error in measuring the length is $(Deltal)/l=2%$

The error in measuring the acceleration due to gravity is $(Deltag)/g=2%$

So,

$(DeltaT)/T=1/2*2%+1/2*2%=2%$