Will You Multiply The Error?

Classical Mechanics Level 3

The side of a cubical block when measured with a vernier caliper is $2.50\text{ cm}$ . The vernier constant is $0.01\text{ cm}$ . The maximum possible error in the area of one face (in $\text{cm}^2$ ) is

\pm 0.01

\pm 0.02

\pm 0.05

\pm 0.10

None of these choices

1 solution

Anandhu Raj
Mar 16, 2016

We Know that area of one face of cubical block, $A={ l }^{ 2 }$

Differentiating with $l$

$\Rightarrow \frac { dA }{ dl } =2l$

$\Rightarrow dA=2l.dl$

$\Rightarrow \Delta A=2l\Delta l$

Now, given $l=2.50$ cm and $\Delta l=0.01$ . Substituting the given values in equation,

$\Rightarrow \Delta A=2\times 2.50\times 0.01=0.05$

Therefore maximum possible error $=\pm 0.05$

Will You Multiply The Error?

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