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AIIMS 2017

Exam: AIIMS
Year: 2017
Subject: Physics
Chapter: Mathematics in Physics

AIIMS 2017 · Physics · Mathematics in Physics

A physical quantity X is given by X= 2 k^3 l^2 m n The percentage...

A physical quantity

X

is given by

X=\frac{2 k^3 l^2}{m \sqrt{n}}

The percentage error in the measurements of

k

,

l, m

and

n

are

1 \%, 2 \%, 3 \%

and

4 \%

respectively. The value of

X

is uncertain by

Options

A $8 \%$
B $10 \%$
C $12 \%$
Dnone of these

Correct answer

C. $12 \%$

Step-by-step solution

\begin{aligned} & \text{ : Given : } X=\frac{2 k^3 l^2}{m \sqrt{n}} \\ & \frac{\Delta X}{X}=3 \frac{\Delta k}{k}+2 \frac{\Delta l}{l}+\frac{\Delta m}{m}+\frac{1}{2} \frac{\Delta n}{n}\end{aligned}

Percentage error in

X

\begin{aligned} \frac{\Delta X}{X} & \times 100=\left(3 \frac{\Delta k}{k}+2 \frac{\Delta l}{l}+\frac{\Delta m}{m}+\frac{1}{2} \frac{\Delta n}{n}\right) \times 100 \\ & =3 \times 1 \%+2 \times 2 \%+3 \%+\frac{1}{2} \times 4 \% \\ & =3 \%+4 \%+3 \%+2 \%=12 \%\end{aligned}

$

Hence, the value of

X

is uncertain by

12 \%$.

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