Dimensions PYQs: JEE Mains Physics – Page 2

51. 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

52. 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

53. 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

54. 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

55. 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

56. 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

57. 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

58. \(\left(P+\frac{a}{V^2}\right)(V-b)=R T\) 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

59. 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

60. 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

61. 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

62. 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

63. 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

64. 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

65. 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

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

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

68. 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

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

70. 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

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

72. 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

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

74. 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

75. Which of the following physical quantities have the same dimensions? 2022 Hard

76. If \(C\) and \(V\) represent capacity and voltage respectively then what are the dimensions of \(\lambda,\) where \(\frac{ C }{ V }=\lambda ?\) 2021 Hard

77. If e is the electronic charge, \(c\) is the speed of light in free space and \(h\) is Planck's constant, the quantity \(\frac{1}{4 \pi \varepsilon_{0}} \frac{| e |^{2}}{h c}\) has dimensions of ....... 2021 Hard

78. If \({E}, {L}, {m}\) and \({G}\) denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of \({P}\) in the formula \({P}={EL}^{2} {m}^{-5} {G}^{-2}\) are 2021 Medium

79. If force \(({F})\), length \(({L})\) and time \(({T})\) are taken as the fundamental quantities. Then what will be the dimension of density 2021 Hard

80. If time \((t)\), velocity \((u)\), and angular momentum \((I)\) are taken as the fundamental units. Then the dimension of mass \(({m})\) in terms of \({t}, {u}\) and \({I}\) is 2021 Medium

81. If velocity \([V],\) time \([T]\) and force \([F]\) are chosen as the base quantities, the dimensions of the mass will be 2021 Medium

82. In a typical combustion engine the work done by a gas molecule is given \(W =\alpha^{2} \beta e ^{\frac{-\beta x ^{2}}{ KT }}\), where \(x\) is the displacement, \(k\) is the Boltzmann constant and \(T\) is the temperature. If \(\alpha\) and \(\beta\) are constants, dimensions of \(\alpha\) will be 2021 Hard

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

List\(-I\)	List\(-II\)
\((a)\) \(h\) (Planck's constant)	\((i)\) \(\left[ M L T ^{-1}\right]\)
\((b)\) \(E\) (kinetic energy)	\((ii)\) \(\left[ M L ^{2} T ^{-1}\right]\)
\((c)\) \(V\) (electric potential)	\((iii)\) \(\left[ M L ^{2} T ^{-2}\right]\)
\((d)\) \(P\) (linear momentum)	\(( iv )\left[ M L ^{2} I ^{-1} T ^{-3}\right]\)

Choose the correct answer from the options given below 2021 Medium

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

List\(-I\)	List\(-II\)
\((a)\) Magnetic Induction	\((i)\) \({ML}^{2} {T}^{-2} {A}^{-1}\)
\((b)\) Magnetic Flux	\((ii)\) \({M}^{0} {L}^{-1} {A}\)
\((c)\) Magnetic Permeability	\((iii)\) \({MT}^{-2} {A}^{-1}\)
\((d)\) Magnetization	\((iv)\) \({MLT}^{-2} {A}^{-2}\)

Choose the most appropriate answer from the options given below: 2021 Medium

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

List\(-I\)	List\(-II\)
\((a)\) Torque	\((i)\) \({MLT}^{-1}\)
\((b)\) Impulse	\((ii)\) \({MT}^{-2}\)
\((c)\) Tension	\((iii)\) \({ML}^{2} {T}^{-2}\)
\((d)\) Surface Tension	\((iv)\) \({MI} {T}^{-2}\)

Choose the most appropriate answer from the option given below : 2021 Medium

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

List\(-I\)	List\(-II\)
\((a)\) Capacitance, \(C\)	\((i)\) \({M}^{1} {L}^{1} {T}^{-3} {A}^{-1}\)
\((b)\) Permittivity of free space, \(\varepsilon_{0}\)	\((ii)\) \({M}^{-1} {L}^{-3} {T}^{4} {A}^{2}\)
\((c)\) Permeability of free space, \(\mu_{0}\)	\((iii)\) \({M}^{-1} L^{-2} T^{4} A^{2}\)
\((d)\) Electric field, \(E\)	\((iv)\) \({M}^{1} {L}^{1} {T}^{-2} {A}^{-2}\)