JEE PHYSICS MCQ: UNITS & MEASUREMENTS

1 Medium

1 of 1

Analyzing +4 | -1

A thin

1 \mathrm{~m}

long rod has a radius of

5 \mathrm{~mm}

. A force of

50 \pi \, \mathrm{kN}

is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is

0.01 \mathrm{~mm}

, which of the following statements is false?

View answer and explanation

Correct option: A

The maximum value of

Y

that can be determined is

10^{14} \mathrm{~N} / \mathrm{m}^2

Option A (The maximum value of

Y

that can be determined is

10^{14} \mathrm{~N} / \mathrm{m}^2

) is false because the calculated Young's modulus is significantly lower than this value, given the provided parameters and uncertainties.

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\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