Question

Question #47b8a

Answer 1

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%`