Question #47b8a

1 Answer
Dec 26, 2017

Answer:

See the explanation below

Explanation:

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%#