STD 11 - Units,dimensions… PYQs: JEE Mains Physics

101. Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\) Assertion \(A\) : A spherical body of radius \((5 \pm 0.1)\) \(mm\) having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is \(4\,\%\). Reason \(R\) : The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius. In the light of the above statements, choose the correct answer from the options given below on : 2023 Medium

102. Given below are two statements : Statements \(I\) : Astronomical unit \((Au)\). Parsec \((Pc)\) and Light year \((ly)\) are units for measuring astronomical distances. Statements \(II:\) \(Au < Parsec ( Pc ) < ly\) In the light of the above statements. choose the most appropriate answer from the options given below: 2023 Medium

103. If \(R , X _{ L }\). and \(X _{ C }\) represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless: 2023 Easy

104. If speed \((V)\), acceleration \((A)\) and force \((F)\) are considered as fundamental units, the dimension of Young’s modulus will be 2023 Hard

105. If the velocity of light \(c\), universal gravitational constant \(G\) and planck's constant \(h\) are chosen as fundamental quantities. The dimensions of mass in the new system is 2023 Hard

106. In a screw gauge, there are \(100\) divisions on the circular scale and the main scale moves by \(0.5\,mm\) on a complete rotation of the circular scale. The zero of circular scale lies \(6\) divisions below the line of graduation when two studs are brought in contact with each other. When a wire is placed between the studs, \(4\) linear scale divisions are clearly visible while \(46^{\text {th }}\) division the circular scale coincide with the reference line. The diameter of the wire is \(...........\times 10^{-2}\,mm\) 2023 Hard

107. In an experiment with Vernier callipers of least count \(0.1\,mm\), when two jaws are joined together the zero of Vernier scale lies right to the zero of the main scale and \(6^{\text {th }}\) division of Vernier scale coincides with the main scale division. While measuring the diameter of a spherical bob, the zero of vernier scale lies in between \(3.2\,cm\) and \(3.3\,cm\) marks, and \(4^{\text {th }}\) division of vernier scale coincides with the main scale division. The diameter of bob is measured as \(.......\,cm\) 2023 Medium

108. In the equation \(\left[X+\frac{a}{Y^2}\right][Y-b]= R T, X\) is pressure, \(Y\) is volume, \(R\) is universal gas constant and \(T\) is temperature. The physical quantity equivalent to the ratio \(\frac{a}{b}\) is 2023 Hard

109. Match List \(I\) with List \(II\)

LIST\(-I\)	LIST\(-II\)
\((A)\) Surface tension	\((I)\) \(Kg m ^{-1} s ^{-1}\)
\((B)\) Pressure	\((II)\) \(Kg ms^{-1 }\)
\((C)\) Viscosity	\((III)\) \(Kg m ^{-1} s ^{-2}\)
\((D)\) Impulse	\((IV)\) \(Kg s ^{-2}\)

Choose the correct answer from the options given below : 2023 Medium

110. Match List \(I\) with List \(II\)

List \(I\)	List \(II\)
\((A)\) Young's Modulus \((Y)\)	\((I)\) \(\left[ M L ^{-1} T ^{-1}\right]\)
\((B)\) Co-efficient of Viscosity \((\eta)\)	\((II)\) \(\left[ M L ^2 T ^{-1}\right]\)
\((C)\) Planck's Constant \((h)\)	\((III)\) \(\left[ M L ^{-1} T ^{-2}\right]\)
\((D)\) Work Function \((\phi)\)	\((IV)\) \(\left[ M L ^2 T ^{-2}\right]\)

Choose the correct answer from the options given below: 2023 Medium

111. Match List\(-I\) with List\(-II\).

List\(-I\)	List\(-II\)
\((A)\) Angular momentum	\((I)\) \(\left[ ML ^2 T ^{-2}\right]\)
\((B)\) Torque	\((II)\) \(\left[ ML ^{-2} T ^{-2}\right]\)
\((C)\) Stress	\((III)\) \(\left[ ML ^2 T ^{-1}\right]\)
\((D)\) Pressure gradient	\((IV)\) \(\left[ ML ^{-1} T ^{-2}\right]\)

Choose the correct answer from the options given below: 2023 Medium

112. Match List \(I\) with List \(II\)

LIST\(-I\)	LIST\(-II\)
\((A)\) Torque	\((I)\) \(ML ^{-2} T ^{-2}\)
\((B)\) Stress	\((II)\) \(ML ^2 T ^{-2}\)
\((C)\) Pressure of gradient	\((III)\) \(ML ^{-1} T ^{-1}\)
\((D)\) Coefficient of viscosity	\((IV)\) \(ML ^{-1} T ^{-2}\)

Choose the correct answer from the options given below 2023 Medium

113. Match List \(I\) with List \(II\)

List \(I\)	List \(II\)
\(A\) Spring constant	\(I\) \((T ^{-1})\)
\(B\) Angular speed	\(II\) \((MT ^{-2})\)
\(C\) Angular momentum	\(III\) \((ML ^2)\)
\(D\) Moment of Inertia	\(IV\) \((ML ^2 T ^{-1})\)

Choose the correct answer from the options given below 2023 Medium

114. Match List \(I\) with List \(II\) :

List \(I\) (Physical Quantity)	List \(II\) (Dimensional Formula)
\((A)\) Pressure gradient	\((I)\) \(\left[ M ^0 L ^2 T ^{-2}\right]\)
\((B)\) Energy density	\((II)\) \(\left[ M ^1 L ^{-1} T ^{-2}\right]\)
\((C)\) Electric Field	\((III)\) \(\left[ M ^1 L ^{-2} T ^{-2}\right]\)
\((D)\) Latent heat	\((IV)\) \(\left[ M ^1 L ^1 T ^{-3} A ^{-1}\right]\)

Choose the correct answer from the options given below: 2023 Medium

115. \(\left(P+\frac{a}{V^2}\right)(V-b)=R T\) represents the equation of state of some gases. Where \(P\) is the pressure, \(V\) is the volume, \(T\) is the temperature and \(a, b, R\) are the constants. The physical quantity, which has dimensional formula as that of \(\frac{b^2}{a}\), will be 2023 Hard

116. The equation of a circle is given by \(x^2+y^2=a^2\), where \(a\) is the radius. If the equation is modified to change the origin other than \((0,0)\), then find out the correct dimensions of \(A\) and \(B\) in a new equation: \((x-A t)^2+\left(y-\frac{t}{B}\right)^2=a^2\).The dimensions of \(t\) is given as \(\left[ T ^{-1}\right]\). 2023 Medium

117. The frequency \((v)\) of an oscillating liquid drop may depend upon radius \((r)\) of the drop, density \((\rho)\) of liquid and the surface tension \((s)\) of the liquid as : \(v=r^{ a } \rho^{ b } s ^{ c }\). The values of \(a , b\) and \(c\) respectively are 2023 Medium

118. The speed of a wave produced in water is given by \(v=\lambda^a g^b \rho^c\). Where \(\lambda\), g and \(\rho\) are wavelength of wave, acceleration due to gravity and density of water respectively. The values of \(a , b\) and \(c\) respectively, are 2023 Medium

119. Two resistances are given as \(R _1=(10 \pm 0.5)\,\Omega\) and \(R_2=(15 \pm 0.5)\, \Omega\). The percentage error in the measurement of equivalent resistance when they are connected in parallel is 2023 Hard

120. A screw gauge of pitch \(0.5\,mm\) is used to measure the diameter of uniform wire of length \(6.8\,cm\), the main scale reading is \(1.5\,mm\) and circular scale reading is \(7\). The calculated curved surface area of wire to appropriate significant figures is \(......cm^2\) . [Screw gauge has \(50\) divisions on the circular scale] 2022 Hard

121. A sliver wire has mass \((0.6 \pm 0.006) \; g\), radius \((0.5 \pm 0.005) \; mm\) and length \((4 \pm 0.04) \; cm\). The maximum percentage error in the measurement of its density will be \(......\,\%\) 2022 Medium

122. A student in the laboratory measures thickness of a wire using screw gauge. The readings are \(1.22\,mm , 1.23\,mm , 1.19\,mm\) and \(1.20\,mm\). The percentage error is \(\frac{ x }{121} \%\). The value of \(x\) is .............. 2022 Medium

123. A torque meter is calibrated to reference standards of mass, length and time each with \(5 \%\) accuracy. After calibration, the measured torque with this torque meter will have net accuracy of\(............\%\) 2022 Medium

124. A travelling microscope has \(20\) divisions per \(cm\) on the main scale while its Vernier scale has total \(50\) divisions and \(25\) Vernier scale divisions are equal to \(24\) main scale divisions, what is the least count of the travelling microscope \(..........\,cm\) 2022 Medium

125. A travelling microscope is used to determine the refractive index of a glass slab. If \(40\) divisions are there in \(1 \; cm\) on main scale and \(50\) Vernier scale divisions are equal to \(49\) main scale divisions, then least count of the travelling microscope is \(\dots \; \times 10^{-6} \; m\) 2022 Medium

126. An expression for a dimensionless quantity \(P\) is given by \(P=\frac{\alpha}{\beta} \log _{e}\left(\frac{ kt }{\beta x }\right)\); where \(\alpha\) and \(\beta\) are constants, \(x\) is distance ; \(k\) is Boltzmann constant and \(t\) is the temperature. Then the dimensions of \(\alpha\) will be 2022 Medium

127. An expression of energy density is given by \(u=\frac{\alpha}{\beta} \sin \left(\frac{\alpha x}{k t}\right)\), where \(\alpha, \beta\) are constants, \(x\) is displacement, \(k\) is Boltzmann constant and \(t\) is the temperature. The dimensions of \(\beta\) will be. 2022 Hard

128. For \(z=a^{2} x^{3} y^{\frac{1}{2}}\), where \(a\) is a constant. If percentage error in measurement of \(x\) and \(y\) are \(4 \%\) and \(12 \%\), respectively, then the percentage error for \(z\) will be \(%\) 2022 Easy

129. Given below are two statements: One is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\) : Product of Pressure \((P)\) and time \((t)\) has the same dimension as that of coefficient of viscosity. Reason \(R\) : Coefficient of viscosity \(=\frac{\text { Force }}{\text { Velocity gradient }}\) Question : Choose the correct answer from the options given below 2022 Medium

130. Given below are two statements: One is labelled as Assertion \((A)\) and other is labelled as Reason \((R)\). Assertion \((A)\) : Time period of oscillation of a liquid drop depends on surface tension \((S)\), if density of the liquid is \(p\) and radius of the drop is \(r\), then \(T = k \sqrt{ pr ^{3} / s ^{3 / 2}}\) is dimensionally correct, where \(K\) is dimensionless. Reason \((R)\): Using dimensional analysis we get \(R.H.S.\) having different dimension than that of time period. In the light of above statements, choose the correct answer from the options given below. 2022 Medium

131. Identify the pair of physical quantities that have same dimensions 2022 Medium

132. Identify the pair of physical quantities which have different dimensions 2022 Medium

133. If \(L , C\) and \(R\) are the self inductance, capacitance and resistance respectively, which of the following does not have the dimension of time? 2022 Medium

134. If momentum \([ P ]\), area \([ A ]\) and time \([ T ]\) are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is : 2022 Medium

135. If \(Z=\frac{A^{2} B^{3}}{C^{4}}\), then the relative error in \(Z\) will be 2022 Easy

136. In a Vernier Calipers. \(10\) divisions of Vernier scale is equal to the \(9\) divisions of main scale. When both jaws of Vernier calipers touch each other, the zero of the Vernier scale is shifted to the left of \(zero\) of the main scale and \(4^{\text {th }}\) Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to \(1\,mm\). While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between \(30\) and \(31\) divisions of main scale reading and \(6^{\text {th }}\) Vernier scale division exactly. coincides with the main scale reading. The diameter of the spherical body will be \(.......cm\) 2022 Hard

137. In a vernier callipers, each \(cm\) on the main scale is divided into \(20\) equal parts. If tenth vernier scale division coincides with nineth main scale division. Then the value of vernier constant will be \(\dots \; \times 10^{-2} \;mm\) 2022 Medium

138. In an experiment of determine the Young's modulus of wire of a length exactly \(1\; m\), the extension in the length of the wire is measured as \(0.4\,mm\) with an uncertainty of \(\pm 0.02\,mm\) when a load of \(1\,kg\) is applied. The diameter of the wire is measured as \(0.4\,mm\) with an uncertainty of \(\pm 0.01\,mm\). The error in the measurement of Young's modulus \((\Delta Y)\) is found to be \(x \times 10^{10}\,Nm ^{-2}\). The value of \(x\) is \(\left[\right.\) Take \(\left.g =10\,m / s ^{2}\right]\) 2022 Hard

139. In an experiment to find acceleration due to gravity \((g)\) using simple pendulum, time period of \(0.5\,s\) is measured from time of \(100\) oscillation with a watch of \(1\;s\) resolution. If measured value of length is \(10\; cm\) known to \(1\; mm\) accuracy. The accuracy in the determination of \(g\) is found to be \(x \%\). The value of \(x\) is 2022 Medium

140. In an experiment to find out the diameter of wire using screw gauge, the following observation were noted. \((a)\) Screw moves \(0.5\,mm\) on main scale in one complete rotation \((b)\) Total divisions on circular scale \(=50\) \((c)\) Main scale reading is \(2.5\,mm\) \((d)\) \(45^{\text {th }}\) division of circular scale is in the pitch line \((e)\) Instrument has \(0.03 \;mm\) negative error Then the diameter of wire is \(...........\,mm\)

2022 Medium

141. In Vander Waals equation \(\left[ P +\frac{ a }{ V ^{2}}\right][ V - b ]= RT\); \(P\) is pressure, \(V\) is volume, \(R\) is universal gas constant and \(T\) is temperature. The ratio of constants \(\frac{a}{b}\) is dimensionally equal to ................. 2022 Medium

142. Match List \(I\) with List \(II\).

List \(I\)	List \(II\)
\((A)\) Torque	\((I)\) \(Nms^{-1}\)
\((B)\) Stress	\((II)\) \(J\,kg^{-1}\)
\((C)\) Latent Heat	\((III)\) \(Nm\)
\((D)\) Power	\((IV)\) \(Nm^{-2}\)

Choose the correct answer from the options below. 2022 Medium

143. The dimension of mutual inductance is ............ 2022 Medium

144. The dimensions of \(\left(\frac{ B ^{2}}{\mu_{0}}\right)\) will be. (if \(\mu_{0}\) : permeability of free space and \(B\) : magnetic field) 2022 Medium

145. The distance of the Sun from earth is \(1.5 \times 10^{11} \,m\) and its angular diameter is \((2000) \,s\) when observed from the earth. The diameter of the Sun will be ........... 2022 Medium

146. The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are \(1 \%, 2 \%\) and \(3 \%\) respectively. The maximum percentage error in the detection of the dissipated heat will be 2022 Easy

147. The one division of main scale of vernier callipers reads \(1\,mm\) and \(10\) divisions of Vernier scale is equal to the \(9\) divisions on main scale. When the two jaws of the instrument touch each other the \(zero\) of the Vernier lies to the right of \(zero\) of the main scale and its fourth division coincides with a main scale division. When a spherical bob is tightly placed between the two jaws, the \(zero\) of the Vernier scale lies in between \(4.1\,cm\) and \(4.2\,cm\) and \(6^{\text {th }}\) Vernier division coincides with a main scale division. The diameter of the bob will be \(.............10^{-2}\,cm\) 2022 Hard

148. The \(SI\) unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be .............. 2022 Medium

149. The vernier constant of Vernier callipers is \(0.1 \,mm\) and it has zero error of \((-0.05) \,cm\). While measuring diameter of a sphere, the main scale reading is \(1.7 \,cm\) and coinciding vernier division is \(5\). The corrected diameter will be ........... \(\times 10^{-2} \,cm\) 2022 Medium

150. Velocity \((v)\) and acceleration \((a)\) in two systems of units \(1\) and \(2\) are related as \(V _{2}=\frac{ n }{ m ^{2}} v _{1}\) and \(a_{2}=\frac{a_{1}}{m n}\) respectively. Here \(m\) and \(n\) are constants. The relations for distance and time in two systems respectively are 2022 Hard

STD 11 - Units,dimensions and measurement PYQs: JEE Mains Physics – Page 3

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