Question

if error in measuring the distance of a planet from sun is 0.4% and in measuring the mass of sun is 0.6% then error in measuring time period of planet around sun is​

Answer 1

Answer:

1.8%

Explanation:

see in the image the solution

Answer 2

Given :

Error in measuring the distance of a planet from sun is 0.4 % .

Error in measuring the mass of sun is 0.6 % .

To Find :

The error in measuring time period of planet around sun .

Solution :

Time period is given by :

$T=\dfrac{4\pi^2r^3}{GM}$

Therefore , error is measuring  time period of planet around sun is​ :

$\dfrac{\Delta T}{T}= 3\dfrac{\Delta r}{r}+\dfrac{\Delta M}{M}$      .... ( 1 )

Here , $\dfrac{\Delta r}{r}=0.4 \%$ and $\dfrac{\Delta M}{M}=0.6\ \%$ .

Putting these value in equation 1 .

We get :

$\dfrac{\Delta T}{T}= (3\times 0.4)+0.6\\\\\dfrac{\Delta T}{T}=1.8\ \%$

Therefore , error in measuring time period of planet around sun is​ 1.8 % .

Learn More :

Errors and Measurements

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