The pressure on a circular plate is measured by measuring the force...

The pressure on a circular plate is measured by measuring the force on the plate and the radius of the plate. If the errors in measurement of the force and the radius are

5 \%

and

3 \%

respectively, the percentage of error in the measurement of pressure is

Options

A $8$
B $14$
C $11$
D $12$

Correct answer

C. $11$

Step-by-step solution

We have

\begin{aligned} & p=\frac{F}{A}=\frac{F}{\pi R^2} \\ & \text { So, } \frac{\Delta p}{p} \times 100=\frac{\Delta F}{F} \times 100+2 \frac{\Delta R}{R} \times 100 \\ & =5+2(3)=5+6=11 \\ & \Rightarrow \frac{\Delta p}{p} \times 100=11 \% \end{aligned}

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