Question 3 :
Which of the following physical quantities has neither dimensions nor unit?
Question 6 :
The thrust developed by a rocket-motor is given by {tex} \mathrm { F } = \mathrm { mv } + \mathrm { A } \left( \mathrm { P } _ { 1 } - \mathrm { P } _ { 2 } \right) {/tex} where {tex} \mathrm { m } {/tex} is the mass of the gas ejected per unit time, {tex}\mathrm v{/tex} is velocity of the gas, {tex} \mathrm { A } {/tex} is area of cross-section of the nozzle, {tex} \mathrm { P } _ { 1 } {/tex} and {tex} \mathrm { P } _ { 2 } {/tex} are the pressures of the exhaust gas and surrounding atmosphere. The formula is dimensionally
Question 7 :
The resistance {tex} R {/tex} of a wire is given by the relation {tex} R = \frac { \rho \ell } { \pi r ^ { 2 } } . {/tex} Percentage error in the measurement of {tex} \rho , \ell {/tex} and {tex} r {/tex} is {tex} 1 \% , 2 \% {/tex} and {tex} 3 \% {/tex} respectively. Then the percentage error in the measurement of {tex} R {/tex} is
Question 9 :
{tex} \mathrm { E } , \mathrm { m } , \mathrm { J } {/tex} and {tex} \mathrm { G } {/tex} denote energy, mass, angular momentum and gravitational constant respectively, then the unit of {tex} \frac { \mathrm { E } \mathrm { J } ^ { 2 } } { \mathrm { m } ^ { 5 } \mathrm { G } ^ { 2 } } {/tex} is
Question 11 :
Area of a square is {tex} ( 100 \pm 2 ) \mathrm { m } ^ { 2 } . {/tex} Its side is
Question 12 :
Relative density of a metal may be found with the help of spring balance. In air the spring balance reads {tex} ( 5.00 \pm 0.05 ) {/tex} N and in water it reads {tex} ( 4.00 \pm 0.05 ) \mathrm { N } {/tex}. Then, the relative density along with the maximum permissible percentage error would be
Question 13 :
If electronic charge e, electron mass {tex} \mathrm { m } {/tex}, speed of light in vacuum {tex} \mathrm { c } {/tex} and Planck's constant {tex} \mathrm { h } {/tex} are taken as fundamental quantities, the permeability of vacuum {tex} \mu _ { 0 } {/tex} can be expressed in units of
Question 14 :
The solar constant is defined as the energy incident per unit area per second. The dimensional formula for solar constant is
Question 15 :
Which one of the following is not a unit of Young’s modulus?
Question 16 :
In order to measure physical quantities in the sub-atomic world, the quantum theory often employs energy [E], angular momentum [J] and velocity [ c] as fundamental dimensions instead of the usual mass, length and time. Then, the dimension of pressure in this theory is
Question 17 :
Mass of a body is {tex} 210 \mathrm { gm } {/tex} and its density is {tex} 7.981 \mathrm { g } / \mathrm { cm } ^ { 3 } {/tex} what will be its volume, with regard to significant digits?
Question 18 :
Diameter of a steel ball is measured using a Vernier callipers which has divisions of {tex} 0.1 \mathrm { cm } {/tex} on its main scale (MS) and {tex} 10 {/tex} divisions of its vernier scale (VS) match {tex} 9 {/tex} divisions on the main scale. Three such measurements for a ball are given below:<br>{tex} \begin{array} { | c | c | c | } \hline \text { S.No. } & { \mathrm { MS } ( \mathrm { cm } ) } & { \text { VS divisions } } \\ \hline 1 & { 0.5 } & { 8 } \\ \hline 2 . & { 0.5 } & { 4 } \\ \hline 3 . & { 0.5 } & { 6 } \\ \hline \end{array} {/tex}<br>If the zero error is {tex} - 0.03 \mathrm { cm } , {/tex} then mean corrected diameter is
Question 20 :
{tex} \begin{array} { l l } { \text { Column I } } & { \text { Column II } } \\ { \text { (A) Length } } & { \text { (1) burette } } \\ { \text { (B) Volume } } & { \text { (2) Vernier callipers } } \\ { \text { (C) Diameter of a thin wire } } & { \text { (3) screw gauge } } \\ { \text { (D) Mass } } & { \text { (4) common balance } } \end{array} {/tex}
