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Question

Physics Question on Units and measurement

A physical quantity X is given by X=2k3l2mnX=\frac{2k^{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

A

0.08

B

0.1

C

0.12

D

none of these

Answer

0.12

Explanation

Solution

Given : X=2k3l2mnX = \frac{2k^{3}l^{2}}{m\sqrt{n}} ΔXX×100=(3Δkk+2Δll+Δmm+12Δnn)×100\therefore\quad \frac{\Delta X}{X}\times100=\left(3 \frac{\Delta k}{k}+2 \frac{\Delta l}{l}+\frac{\Delta m}{m}+\frac{1}{2} \frac{\Delta n}{n}\right)\times100 =3?1%+2?2%+3%+12×4%\quad= 3 ? 1\% + 2 ? 2\% + 3\% +\frac{1}{2}\times4\% =3%+4%+3%+2%=12%\quad= 3\% + 4\% + 3\% + 2\% = 12\% Hence, the value of X is uncertain by 12%.