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

Showing 1–50 of 236 questions

1. 1. A ball of radius r and density \(\rho\) dropped through a viscous liquid of density \(\sigma\) and viscosity \(\eta\) attains its terminal velocity at time t , given by \(t = A \rho^{ a } r ^{ b } \eta^{ c } \sigma^{ d }\), where A is a constant and a , b c and d are integers. The value of \(\frac{b+c}{a+d}\) is ___________. 2026 Hard
2. 2. A new unit \((\alpha)\) of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of \(\alpha\) units if light takes \(6\) min. \(40\) s to cover this distance? 2026 Easy
3. 3. Consider a modified Bernoulli equation.
   \(\left( P +\frac{ A }{ Bt ^2}\right)+\rho g ( h + Bt )+\frac{1}{2} \rho V^2=\) constant
   If \(t\) has the dimension of time then the dimensions of A and B are _________ , _________ respectively. 2026 Hard
4. 4. Consider the equation \(H = \dfrac{x^p \epsilon^q E^r}{t^s}\), where \(H=\) magnetic field; \(E=\) electric field, \(\epsilon=\) permittivity, \(x=\) distance, \(t=\) time. The values of \(p, q, r\) and \(s\) respectively are: 2026 Hard
5. 5. Dimensions of universal gravitational constant \((G)\) in terms of Planck's constant \((h)\), distance \((L)\), mass \((M)\) and time \((T)\) are _______. 2026 Medium
6. 6. Four persons measure the length of a rod as 20.00 cm, 19.75 cm, 17.01 cm and 18.25 cm. The relative error in the measurement of average length of the rod is : 2026 Medium
7. 7. If \(\in\), \( E \) and \( t \) represent the free space permittivity, electric field and time respectively, then the unit of \( \frac{eE}{t} \) will be : 2026 Medium
8. 8. In a screw gauge the zero of main scale reference line coincides with the fifth division of the circular scale when two studs are in contact. There are \(100\) divisions in circular scale and pitch of screw gauge is \(0.1\) mm. When diameter of a sphere is measured, the reading of main scale is \(5\) mm and \(50^{\text{th}}\) division of circular scale coincides with the reference line of main scale. The diameter of sphere is _______ mm. 2026 Medium
9. 9. In a screw gauge, the zero of the circular scale lies 3 divisions above the horizontal pitch line when their metallic studs are brought in contact. Using this instrument thickness of a sheet is measured. If pitch scale reading is 1 mm and the circular scale reading is 51 then the correct thickness of the sheet is ___________ mm.
   [Assume least count is 0.01 mm ] 2026 Medium
10. 10. In a screw gauge when the circular scale is given five complete rotations it moves linearly by \(2.5\) mm. If the circular scale has \(100\) divisions, the least count of screw gauge is _____ mm. 2026 Easy
11. 11. In a Vernier calipers, when both jaws touch each other, zero of the Vernier scale is shifted to the right of zero of the main scale and \(7^{\text{th}}\) Vernier division coincides with a main scale reading. If the value of \(1\) main scale division is \(1\) mm and there are \(10\) Vernier scale divisions, then the Vernier caliper has 2026 Medium
12. 12. In a vernier callipers, 50 vernier scale divisions are equal to 48 main scale divisions. If one main scale division \(=0.05 mm\), then the least count of the vernier callipers is _________ mm. 2026 Medium
13. 13. In an experiment, a set of reading are obtained \(-1.24 mm, 1.25 mm, 1.23 mm, 1.21 mm\). The expected least count of the instrument used in recording these readings is ___________ mm. 2026 Medium
14. 14. In an experiment the values of two spring constants were measured as \(k _1=(10 \pm 0.2) N / m\)
    and \(k _2=(20 \pm 0.3) N / m\). If these springs are connected in parallel, then the percentage error in equivalent spring constant is : 2026 Easy
15. 15. In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are noted as \(10\text{ V}\) and \(5\text{ A}\), respectively. The least counts of voltmeter and ammeter are \(500\text{ mV}\) and \(200\text{ mA}\), respectively. The estimated error in the resistance measurement is _______ \(\Omega\). 2026 Medium
16. 16. Keeping the significant figures in view, the sum of the physical quantities \(52.01 m, 153.2 m\) and 0.123 m is : 2026 Medium
17. 17. \(L\), \(C\) and \(R\) represents physical quantities inductance, capacitance and resistance respectively. The dimensional formula \(ML^2 T^{-4} A^{-2}\) corresponds to __________. 2026 Hard
18. 18. Match List - I with List - II.

    List - I	List - II
    A. Boltzmann constant	I. \([M^{-1}L^3T^{-2}]\)
    B. Stefan's constant	II. \([ML^2T^{-1}]\)
    C. Planck's constant	III. \([ML^2T^{-2}K^{-1}]\)
    D. Gravitational constant	IV. \([ML^0T^{-3}K^{-4}]\)

    Choose the correct answer from the options given below : 2026 Medium
19. 19. Match List-I with List-II.
    

    List-I	List-II
    A. Meter (L)	I. \(\sqrt{\dfrac{hc}{G}}\)
    B. Second (S)	II. \(\sqrt{\dfrac{Gh}{c^5}}\)
    C. Kilogram (M)	III. \(\sqrt{\dfrac{K^2L^2c^3}{Gh}}\)
    D. Kelvin (K)	IV. \(\sqrt{\dfrac{Gh}{c^3}}\)

    
    where \(h\) (Planck's constant), \(G\) (gravitational constant) and \(c\) (speed of light in vacuum) as fundamental units.
    Choose the correct answer from the options given below : 2026 Hard
20. 20. Match the LIST-I with LIST-II:

    List-I	List-II
    A. Spring constant	I. \(ML ^2 T^{-2} K^{-1}\)
    B. Thermal conductivity	II. \(ML ^0 T^{-2}\)
    C. Boltzmann constant	III. \(ML ^2 T^{-3} A^{-2}\)
    D. Inductive reactance	IV. \(MLT ^{-3} K^{-1}\)

    Choose the correct answer from the options given below: 2026 Easy
21. 21. Match the LIST-I with LIST-II
    

    List-I	List-II
    A. Planck's constant	I. \(ML^2T^{-2}\)
    B. Stopping potential	II. \(T^{-1}\)
    C. Work function	III. \(ML^2T^{-1}\)
    D. Threshold frequency	IV. \(ML^2T^{-3}A^{-1}\)

    
    Choose the correct answer from the options given below: 2026 Medium
22. 22. The density \(\rho\) of a uniform cylinder is determined by measuring its mass \(m\), length \(l\) and diameter \(d\). The measured values of \(m\), \(l\) and \(d\) are \(97.42 \pm 0.02\) g, \(8.35 \pm 0.05\) mm and \(20.20 \pm 0.02\) mm, respectively. Calculated percentage fractional error in \(\rho\) is _______. 2026 Medium
23. 23. The diameter of a wire measured by a screw gauge of least count \(0.001\) cm is \(0.08\) cm. The length measured by a scale of least count \(0.1\) cm is \(150\) cm. When a weight of \(100\) N is applied to the wire, the extension in length is \(0.5\) cm, measured by a micrometer of least count \(0.001\) cm. The error in the measured Young's modulus is \(\alpha \times 10^9\) N/m\(^2\). The value of \(\alpha\) is _______.
    (Ignore the contribution of the load to Young's modulus error calculation) 2026 Hard
24. 24. The potential energy of a particle changes with distance \(x\) from a fixed origin as \(V = \dfrac{A\sqrt{x}}{x + B}\), where \(A\) and \(B\) are constant with appropriate dimensions. The dimensions of \(AB\) are _______. 2026 Easy
25. 25. The time period of a simple harmonic oscillator is \(T =2 \pi \sqrt{\frac{ k }{ m }}\). The measured value of mass (m) of the object is 10 g with an accuracy of 10 mg , and time for 50 oscillations of the spring is found to be 60 s using a watch of 2 s resolution. Percentage error in determination of spring constant( \(k\) ) is ___________ %. 2026 Medium
26. 26. When both jaws of vernier callipers touch each other, zero mark of the vernier scale is right to zero mark of main scale, \(4^{\text {th}}\) mark on vernier scale coincides with certain mark on the main scale. While measuring the length of a cylinder, observer observes 15 divisions on main scale and \(5^{\text {th}}\) division of vernier scale coincides with a main scale division. Measured length of cylinder is ___________ mm. (Least count of Vernier calliper \(= 0.1\ mm\)) 2026 Easy
27. 27. A person measures mass of 3 different particles as \(435.42 \mathrm{~g}, 226.3 \mathrm{~g}\) and 0.125 g. According to the rules for arithmetic operations with significant figures, the additions of the masses of 3 particles will be. 2025 Easy
28. 28. A physical quantity C is related to four other quantities \(\mathrm{p}, \mathrm{q}, \mathrm{r}\) and s as follows \(\mathrm{C}=\frac{\mathrm{pq}^2}{\mathrm{r}^3 \sqrt{\mathrm{~s}}}\)
    The percentage errors in the measurement of \(\mathrm{p}, \mathrm{q}, \mathrm{r}\) and s are \(1 \%, 2 \% 3 \%\) and \(2 \%\) respectively. The percentage error in the measurement of C will be _____\(\%\). 2025 Easy
29. 29. A physical quantity \(Q\) is related to four observables \(a, b, c, d\) as follows :
    \(\mathrm{Q}=\frac{\mathrm{ab}{ }^4}{\mathrm{~cd}}\)
    
    where, \(\mathrm{a}=(60 \pm 3) \mathrm{Pa} ; \mathrm{b}=(20 \pm 0.1) \mathrm{m} ; \mathrm{c}=(40 \pm 0.2) \mathrm{Nsm}^{-2}\) and \(\mathrm{d}=(50 \pm 0.1) \mathrm{m}\), then the percentage error in Q is \(\frac{x}{1000}\), where \(x=\) ________ . 2025 Medium
30. 30. A quantity Q is formulated as \(\mathrm{X}^{-2} \mathrm{Y}^{+\frac{3}{2}} \mathrm{Z}^{-\frac{2}{5}} \cdot \mathrm{X}, \mathrm{Y}\) and Z are independent parameters which have fractional errors of \(0.1,0.2\) and 0.5 , respectively in measurement. The maximum fractional error of Q is _______. 2025 Medium
31. 31. A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5 mm , respectively. Using a specially designed screw gauge which has pitch of 0.75 mm and 15 divisions in the circular scale, you are asked to find the area of the sheet. In this measurement, the maximum fractional error will be \(\frac{x}{100}\) where \(x\) is _________. 2025 Medium
32. 32. For an experimental expression \(y=\frac{32.3 \times 1125}{27.4}\), where all the digits are significant. Then to report the value of \(y\) we should write 2025 Easy
33. 33. For the determination of refractive index of glass slab, a travelling microscope is used whose main scale contains 300 equal divisions equals to 15 cm. The vernier scale attached to the microscope has 25 divisions equals to 24 divisions of main scale. The least count (LC) of the travelling microscope is (in cm) : 2025 Easy
34. 34. Given a charge \(q\), current I and permeability of vacuum \(\mu_0\). Which of the following quantity has the dimension of momentum? 2025 Medium
35. 35. Given below are two statements :
    Statement I : In a vernier callipers, one vernier scale division is always smaller than one main scale division.
    Statement II : The vernier constant is given by one main scale division multiplied by the number of vernier scale divisions.
    In the light of the above statements, choose the correct answer from the options given below. 2025 Easy
36. 36. If \(\mu_0\) and \(\varepsilon_0\) are the permeability and permittivity of free space, respectively, then the dimension of \(\left(\frac{1}{\mu_0 \varepsilon_0}\right)\) is : 2025 Easy
37. 37. If \(\epsilon_0\) denotes the permittivity of free space and \(\Phi_{\mathrm{E}}\) is the flux of the electric field through the area bounded by the closed surface, then dimension of \(\left(\epsilon_0 \frac{\mathrm{~d} \phi_{\mathrm{E}}}{\mathrm{dt}}\right)\) are that of : 2025 Easy
38. 38. If \(B\) is magnetic field and \(\mu_0\) is permeability of free space, then the dimensions of \(\left(B / \mu_0\right)\) is 2025 Easy
39. 39. In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of \(\left[M^a L^b T^c\right]\). If \(b=-3\), the value of \(c\) is ________ 2025 Medium
40. 40. In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimension of \(\left[M^P L^{\circ} \mathrm{T}^{\mathrm{R}} \mathrm{A}^{\mathrm{S}}\right]\). The value of P and Q are : 2025 Easy
41. 41. In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of \(\mathrm{M}^{\mathrm{P}} \mathrm{L}^{\mathrm{Q}} \mathrm{T}^{\mathrm{R}} \mathrm{A}^{\mathrm{S}}\), where value of ' Q ' and ' R ' are 2025 Medium
42. 42.

    List - I	List - II
    (A) Heat capacity of body	\(\text{(I) } \mathrm{J} \mathrm{kg}^{-1}\)
    (B) Specific heat capacity of body	\(\text{(II) } \mathrm{JK}^{-1}\)
    (C) Latent heat	\(\text{(III) } \mathrm{J} \mathrm{kg}^{-1} \mathrm{~K}^{-1}\)
    (D) Thermal conductivity	\(\text{(IV) } \mathrm{Jm}^{-1} \mathrm{~K}^{-1} \mathrm{~s}^{-1}\)

    Choose the correct answer from the options given below: 2025 Hard
43. 43. Match List - I with List - II.

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

    Choose\(\text{ }\)the\(\text{ }\)correct\(\text{ }\)answer\(\text{ }\)from\(\text{ }\)the\(\text{ }\)options\(\text{ }\)given\(\text{ }\)below\(\text{ }\): 2025 Easy
44. 44. Match List - I with List - II.
    

    List - I	List - II
    (A) Young’s Modulus	(I) \(M L^{-1} T^{-1}\)
    (B) Torque	(II) \(M L^{-1} T^{-2}\)
    (C) Coefficient of Viscosity	(III) \(M^{-1} L^3 T^{-2}\)
    (D) Gravitational Constant	(IV) \(M L^2 T^{-2}\)

    
    Choose the correct answer from the options given below : 2025 Medium
45. 45. Match List - I with List - II.
    

    List-I	List-II
    (A) Angular Impulse	(I) \(\left[M^0 L^2 T^{-2}\right]\)
    (B) Latent Heat	(II) \(\left[M L^2 T^{-3} A^{-1}\right]\)
    (C) Electrical resistivity	(III) \(\left[M L^2 T^{-1}\right]\)
    (D) Electromotive force	(IV) \(\left[M L^3 T^{-3} A^{-2}\right]\)

    
    2025 Easy
46. 46. Match List-I with List-II.
    

    List-I	List-II
    (A) Mass density	(I) [ML2T-3]
    (B) Impulse	(II) [MLT-1]
    (C) Power	(III) [ML2T0]
    (D) Moment of inertia	(IV) [ML-3T0]

    
    Choose the correct answer from the options given below : 2025 Easy
47. 47. Match List - I with List - II.
    

    List - I	List - II
    (A) Magnetic induction	(I) Ampere meter2
    (B) Magnetic intensity	(II) Weber
    (C) Magnetic flux	(III) Gauss
    (D) Magnetic moment	(IV) Ampere meter

    
    Choose the correct answer from the options given below : 2025 Medium
48. 48. Match List-I with List-II.
    

    List-I (Physical Quantity)	List-II (Dimensional Formula)
    (A) Coefficient of viscosity	(I) [ML0T-3]
    (B) Intensity of wave	(II) [ML-2T-2]
    (C) Pressure gradient	(III) [M-1LT2]
    (D) Compressibility	(IV) [ML-1T-1]

    
    Choose the correct answer from the options given below : 2025 Medium
49. 49. Match the LIST-I with LIST-II

    LIST-I	LIST-II
    (A) Boltzmann constant	I. \(\mathrm{ML}^2 \mathrm{~T}^{-1}\)
    (B) Coefficient of viscosity	II. \(\mathrm{MLT}^{-3} \mathrm{~K}^{-1}\)
    (C) Planck's constant	III. \(\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\)
    (D) Thermal conductivity	IV. \(\mathrm{ML}^{-1} \mathrm{~T}^{-1}\)

    
    Choose the correct answer from the options given below : 2025 Medium
50. 50. Match the LIST-I with LIST-II

    LIST-I	LIST-II
    (A) Gravitational constant	(I) \(\left[\mathrm{LT}^{-2}\right]\)
    (B) Gravitational potential energy	(II) \(\left[\mathrm{L}^2 \mathrm{~T}^{-2}\right]\)
    (C) Gravitational potential	(III) \(\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]\)
    (D) Acceleration due to gravity	(IV) \(\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]\)

    Choose the correct answer from the options given below : 2025 Medium

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