JEE PHYSICS MCQ: UNITS & MEASUREMENTS

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Application +4 | -1

A physical quantity

Q

is found to depend on observables

x, y

, and

z

, obeying relation

Q=x^3 y^2 / z

. The percentage error in the measurements of

x, y

, and

z

are

1 \%, 2 \%

and

4 \%

respectively. What is percentage error in the quantity

Q

View answer and explanation

Correct option: C

11 \%

Option C (

11 \%

) is correct because the percentage error in Q is calculated by summing the percentage errors in x, y, and z, each multiplied by their respective exponents in the relation Q = x³y²/z.

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Assertion :

\sqrt{\frac{\text { Modulus of elasticity }}{\text { Density }}}

has the unit

\mathrm{ms}^{-1} \text {. }

Reason: Acceleration has the dimensions of

\frac{1}{\left(\sqrt{\varepsilon_0 \mu_0}\right) t} \text {. }

The method of dimensional analysis can be used to derive which of the following relations? Statement-I: Dimensions of constant of proportionality of constants can be derived from dimensional method
Statement-II: Numerical value of constant of proportionality can be found from experiments only The dimensions of torque are The physical quantity having the dimensions

\left[ {{\mathrm{M}^{ - 1}}{\mathrm{L}^{ - 3}}{\mathrm{A}^2}{T^3}} \right]

is A quantity X is given by

{\varepsilon _0}L\frac{{\Delta V}}{{\Delta t}},\;

, where

{\varepsilon _0}

is the permittivity of free space, L is a length,

{\Delta V}

is a potential difference and

{\Delta t}

is a time interval. The dimensional formula for X is the same as that of