STD 11 - Units,dimensions and measurement PYQs: JEE Mains Physics – Page 2

Showing 51–100 of 236 questions

51. 51. The dimension of \(\sqrt{\frac{\mu_0}{\epsilon_0}}\) is equal to that of :
    ( \(\mu_0=\) Vacuum permeability and \(\epsilon_0=\) Vacuum permittivity) 2025 Medium
52. 52. The electric flux is \(\phi=\alpha \sigma+\beta \lambda\) where \(\lambda\) and \(\sigma\) are linear and surface charge density, respectively. \(\left(\frac{\alpha}{\beta}\right)\) represents 2025 Easy
53. 53. The energy of a system is given as \(\mathrm{E}(\mathrm{t})=\alpha^3 \mathrm{e}^{-\beta t}\), where t is the time and \(\beta=0.3 \mathrm{~s}^{-1}\). The errors in the measurement of \(\alpha\) and \(t\) are \(1.2 \%\) and \(1.6 \%\), respectively. At \(t=5 \mathrm{~s}\), maximum percentage error in the energy is : 2025 Medium
54. 54. The equation for real gas is given by \(\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}\), where \(\mathrm{P}, \mathrm{V}, \mathrm{T}\) and R are the pressure, volume, temperature and gas constant, respectively. The dimension of \(\mathrm{ab}^{-2}\) is equivalent to that of : 2025 Medium
55. 55. The expression given below shows the variation of velocity \((v)\) with time (t), \(v=\mathrm{At}^2+\frac{\mathrm{Bt}}{\mathrm{C}+\mathrm{t}}\). The dimension of ABC is : 2025 Hard
56. 56. The least count of a screw guage is 0.01 mm . If the pitch is increased by \(75 \%\) and number of divisions on the circular scale is reduced by \(50 \%\), the new least count will be _____ \(\times 10^{-3} \mathrm{~mm}\) 2025 Easy
57. 57. The maximum percentage error in the measurment of density of a wire is [Given, mass of wire \(=(0.60 \pm 0.003) \mathrm{g}\)
    radius of wire \(=(0.50 \pm 0.01) \mathrm{cm}\)
    length of wire \(=(10.00 \pm 0.05) \mathrm{cm}]\) 2025 Medium
58. 58. The pair of physical quantities not having same dimensions is : 2025 Easy
59. 59. The position of a particle moving on \(x\)-axis is given by \(x(t)=A \sin t+B \cos ^2 t+C t^2+D\), where \(t\) is time. The dimension of \(\frac{A B C}{D}\) is 2025 Easy
60. 60. The unit of \(\sqrt{\frac{2 \mathrm{I}}{\epsilon_0 c}}\) is :
    (I = intensity of an electromagnetic wave, \(\mathrm{c}:\) speed of light) 2025 Easy
61. 61. Which one of the following is the correct dimensional formula for the capacitance in F ? \(\mathrm{M}, \mathrm{L}, \mathrm{T}\) and C stand for unit of mass, length, time and charge, 2025 Easy
62. 62. \(10\) divisions on the main scale of a Vernier calliper coincide with \(11\) divisions on the Vernier scale. If each division on the main scale is of \(5\) units, the least count of the instrument is _______. 2024 Hard
63. 63. A force is represented by \(\mathrm{F}=a \mathrm{x}^2+\mathrm{bt}^{1 / 2}\). Where \(\mathrm{x}=\) distance and \(\mathrm{t}=\) time. The dimensions of \(\mathrm{b}^2 / \mathrm{a}\) are _______. 2024 Hard
64. 64. A physical quantity \(Q\) is found to depend on quantities \(a, b, c\) by the relation \(Q=\frac{a^4 b^3}{c^2}\). The percentage error in \(a\), \(b\) and \(c\) are \(3 \%, 4 \%\) and \(5 \%\) respectively. Then, the percentage error in \(\mathrm{Q}\) is _______. 2024 Hard
65. 65. A vernier callipers has \(20\) divisions on the vernier scale, which coincides with \(19^{\text {th }}\) division on the main scale. The least count of the instrument is \(0.1 \mathrm{~mm}\). One main scale division is equal to _______ \(\mathrm{mm}\). 2024 Hard
66. 66. Applying the principle of homogeneity of dimensions, determine which one is correct. where \(\mathrm{T}\) is time period, \(\mathrm{G}\) is gravitational constant, \(M\) is mass, \(r\) is radius of orbit. 2024 Hard
67. 67. Consider two physical quantities A and B related to each other as \(E=\frac{B-x^2}{A t}\) where \(E, x\) and \(t\) have dimensions of energy, length and time respectively. The dimension of \(A B\) is _______. 2024 Hard
68. 68. Given below are two statements : Statement \((I)\) : dimensions of specific heat is \(\left[\mathrm{L}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]\) Statement \((II)\) : dimensions of gas constant is \(\left[\mathrm{ML}^2 \mathrm{~T}^{-1} \mathrm{~K}^{-1}\right]\) 2024 Hard
69. 69. Given below are two statements : \(Statement\) \((I)\) : Planck's constant and angular momentum have same dimensions. \(Statement\) \((II)\) : Linear momentum and moment of force have same dimensions. In the light of the above statements, choose the correct answer from the options given below : 2024 Hard
70. 70. If \(\varepsilon_0\) is the permittivity of free space and \(E\) is the electric field, then \(\varepsilon_0 E^2\) has the dimensions is _______. 2024 Medium
71. 71. If \(50\) Vernier divisions are equal to \(49\) main scale divisions of a travelling microscope and one smallest reading of main scale is \(0.5 \mathrm{~mm}\), the Vernier constant of travelling microscope is _______. 2024 Hard
72. 72. If \(\mathrm{G}\) be the gravitational constant and \(\mathrm{u}\) be the energy density then which of the following quantity have the dimension as that the \(\sqrt{\mathrm{uG}}\)? 2024 Hard
73. 73. If mass is written as \(\mathrm{m}=\mathrm{kc}^{\mathrm{p}} \mathrm{G}^{-1 / 2} \mathrm{~h}^{1 / 2}\) then the value of \(P\) will be _______. (Constants have their usual meaning with \(\mathrm{k}\) a dimensionless constant) 2024 Hard
74. 74. If the percentage errors in measuring the length and the diameter of a wire are \(0.1 \%\) each. The percentage error in measuring its resistance will be _______. 2024 Hard
75. 75. In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its \(4^{\text {th }}\) division coincides exactly with a certain division on main scale. If \(50\) vernier scale divisions equal to \(49\) main scale divisions and zero error in the instrument is \(0.04 \mathrm{~mm}\) then how many main scale divisions are there in \(1 \mathrm{~cm}\) ? 2024 Hard
76. 76. In an expression a \(\times 10^{\mathrm{b}}\) _______. 2024 Easy
77. 77. In finding out refractive index of glass slab the following observations were made through travelling microscope \(50\) vernier scale division \(=\) \(49 \mathrm{MSD} ; 20\) divisions on main scale in each \(\mathrm{cm}\) For mark on paper \(\mathrm{MSR}=8.45 \mathrm{~cm}, \mathrm{VC}=26\) For mark on paper seen through slab \(\mathrm{MSR}=7.12 \mathrm{~cm}, \mathrm{VC}=41\) For powder particle on the top surface of the glass slab \(\mathrm{MSR}=4.05 \mathrm{~cm}, \mathrm{VC}=1\) \((\mathrm{MSR}=\) Main Scale Reading, \(\mathrm{VC}=\) Vernier Coincidence) Refractive index of the glass slab is _______. 2024 Hard
78. 78. Least count of a vernier caliper is \(\frac{1}{20 \mathrm{~N}} \mathrm{~cm}\). The value of one division on the main scale is \(1 \mathrm{~mm}\). Then the number of divisions of main scale that coincide with \(\mathrm{N}\) divisions of vernier scale is _______. 2024 Hard
79. 79. Match List \(-I\) with List \(-II\).

    	List \(-I\)		List \(-II\)
    \(A\).	Coefficient of Viscosity	\(I\).	\([M L^2T^{–2}]\)
    \(B\).	Surface Tension	\(II\).	\([M L^2T^{–1}]\)
    \(C\).	Angular momentum	\(III\).	\([M L^{-1}T^{–1}]\)
    \(D\).	Rotational Kimeatic energy	\(IV\).	\([M L^0T^{–2}]\)

    2024 Hard
80. 80. Match List \(I\) with List \(II\)

    List - \(I\)	List - \(II\)
    \((A)\) Torque	\((I)\) \({\left[\mathrm{M}^1 \mathrm{~L}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-2}\right]}\)
    \((B)\) Magnetic fileld	\((II)\) \(\left[\mathrm{L}^2 \mathrm{~A}^1\right]\)
    \((C)\) Magneti moment	\((III)\) \({\left[\mathrm{M}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]}\)
    \((D)\) permeability of free space	\((IV)\) \(\left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]\)

    Choose the correct answer from the options given below : 2024 Hard
81. 81. Match List - \(I\) with List - \(II\).

    List - \(I\) \((Number)\)	List - \(II\) \((Significant figure)\)
    \((A)\) \(1001\)	\((I)\) \(3\)
    \((B)\) \(010.1\)	\((II)\) \(4\)
    \((C)\) \(100.100\)	\((III)\) \(5\)
    \((D)\) \(0.0010010\)	\((IV)\) \(6\)

    Choose the correct answer from the options given below : 2024 Hard
82. 82. One main scale division of a vernier caliper is equal to \(m\) units. If \(n^{\text {th }}\) division of main scale coincides with \((n+1)^{\mathrm{th}}\) division of vernier scale, the least count of the vernier caliper is _______. 2024 Hard
83. 83. The de-Broglie wavelength associated with a particle of mass \(m\) and energy \(E\) is \(\mathrm{h} / \sqrt{2 m E}\) The dimensional formula for Planck's constant is _______. 2024 Hard
84. 84. The diameter of a sphere is measured using a vernier caliper whose \(9\) divisions of main scale are equal to \(10\) divisions of vernier scale. The shortest division on the main scale is equal to \(1 \mathrm{~mm}\). The main scale reading is \(2 \mathrm{~cm}\) and second division of vernier scale coincides with a division on main scale. If mass of the sphere is \(8.635 \mathrm{~g}\), thedensity of the sphere \(1 \mathrm{~s}\) _______. 2024 Hard
85. 85. The dimensional formula of angular impulse is _______. 2024 Hard
86. 86. The dimensional formula of latent heat is _______. 2024 Hard
87. 87. The equation of state of a real gas is given by \(\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}\), where \(\mathrm{P}, \mathrm{V}\) and \(\mathrm{T}\) are pressure. volume and temperature respectively and \(R\) is the universal gas constant. The dimensions of \(\frac{a}{b^2}\) is similar to that of : 2024 Hard
88. 88. The equation of stationary wave is \(\mathrm{y}=2 \mathrm{a} \sin \left(\frac{2 \pi \mathrm{nt}}{\lambda}\right) \cos \left(\frac{2 \pi \mathrm{x}}{\lambda}\right)\) Which of the following is NOT correct? 2024 Hard
89. 89. The measured value of the length of a simple pendulum is \(20 \mathrm{~cm}\) with \(2 \mathrm{~mm}\) accuracy. The time for \(50\) oscillations was measured to be \(40\) seconds with \(1\) second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is \(\mathrm{N} \%\). The value of \(\mathrm{N}\) is _______. 2024 Hard
90. 90. The radius ( \(\mathrm{r})\), length \((l)\) and resistance \((\mathrm{R})\) of a metal wire was measured in the laboratory as \(\mathrm{r}=(0.35 \pm 0.05) \mathrm{cm}\) \(\mathrm{R}=(100 \pm 10) \mathrm{ohm}\) \(l=(15 \pm 0.2) \mathrm{cm}\) The percentage error in resistivity of the material of the wire is _______. 2024 Hard
91. 91. The resistance \(\mathrm{R}=\frac{\mathrm{V}}{\mathrm{I}}\) where \(\mathrm{V}=(200 \pm 5) \mathrm{V}\) and \(I=(20 \pm 0.2) A\), the percentage error in the measurement of \(R\) is _______. 2024 Hard
92. 92. There are \(100\) divisions on the circular scale of a screw gauge of pitch \(1 \mathrm{~mm}\). With no measuring quantity in between the jaws, the zero of the circular scale lies \(5\) divisions below the reference line. The diameter of a wire is then measured using this screw gauge. It is found the \(4\) linear scale divisions are clearly visible while \(60\) divisions on circular scale coincide with the reference line. The diameter of the wire is _______. 2024 Hard
93. 93. Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as \(4.62 \mathrm{~s}, 4.632 \mathrm{~s}, 4.6 \mathrm{~s}\) and \(4.64 \mathrm{~s}\). The arithmetic mean of these reading in correct significant figure is _______. 2024 Hard
94. 94. What is the dimensional formula of \(a b^{-1}\) in the equation? \(\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}\), where letters have their usual meaning. 2024 Hard
95. 95. While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is \(1 \mathrm{~mm}\) and circular scale reading is equal to \(42\) divisions. Pitch of screw gauge is \(1 \mathrm{~mm}\) and it has \(100\) divisions on circular scale. The diameter of the wire is \(\frac{x}{50} \mathrm{~mm}\). The value of \(x\) is _______. 2024 Hard
96. 96. A body of mass \((5 \pm 0.5) kg\) is moving with a velocity of \((20 \pm 0.4) m / s\). Its kinetic energy will be 2023 Medium
97. 97. A cylindrical wire of mass \((0.4 \pm 0.01)\,g\) has length \((8 \pm 0.04)\,cm\) and radius \((6 \pm 0.03)\,mm\).The maximum error in its density will be \(......\,\%\) 2023 Medium
98. 98. A physical quantity \(P\) is given as \(P=\frac{a^2 b^3}{c \sqrt{d}}\) The percentage error in the measurement of \(a, b, c\) and \(d\) are \(1 \%, 2 \%, 3 \%\) and \(4 \%\) respectively. The percentage error in the measurement of quantity \(P\) will be \(.......\%\) 2023 Easy
99. 99. Dimension of \(\frac{1}{\mu_0 \varepsilon_0}\) should be equal to 2023 Medium
100. 100. Electric field in a certain region is given by \(\overrightarrow{ E }=\left(\frac{ A }{ x ^2} \hat{ i }+\frac{ B }{ y ^3} \hat{ j }\right)\). The \(SI\) unit of \(A\) and \(B\) are 2023 Medium

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