Title 02. UNITS AND MEASUREMENTS (1).pdf ✅

Units and Measurements 1.2The International System of Units 1. The unit of thermal conductivity is (a) Wm−1 K −1 (b) JmK −1 (c) Jm−1 K −1 (d) WmK −1 (2019) 2. The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are (a) kgms −1 (b) kgms −2 (c) kgs −1 (d) kg s (2012) 3. The unit of permittivity of free space, ε0, is (a) coulomb/newton-metre (b) newton-metre 2 / coulomb 2 (c) coulomb 2 / newton-metre 2 (d) coulomb 2 /( newton-metre ) 2 (2004) Accuracy, Precision of Instruments and Errors in Measurement 4. The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are (a) Least count errors (b) Random errors (c) Instrumental errors (d) Personal errors. (2023) 5. A metal wire has mass (0.4 ± 0.002)g, radius (0.3 ± 0.001)mm and length ( 5 ± 0.02 ) cm. The maximum possible percentage error in the measurement of density will nearly be (a) 1.6% (b) 1.4% (c) 1.2% (d) 1.3% (2023) 6. A screw gauge gives the following readings when used to measure the diameter of a wire Main scale reading : 0 mm Circular scale reading : 52 divisions Given that 1 mm on main scale corresponds to 100 divisions on the circular scale. The diameter of the wire from the above data is (a) 0.052 cm (b) 0.52 cm (c) 0.026 cm (d) 0.26 cm (2021) 7. A screw gauge has least count of 0.01 mm and there are 50 divisions in its circular scale. The pitch of the screw gauge is (a) 0.01 mm (b) 0.25 mm (c) 0.5 mm (d) 1.0 mm (2020) 8. In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement X, where X = A 2B 1/2 C1/3D3 , will be (a) 10% (b) (3/13)% (c) 16% (d) −10% (2019) 9. The main scale " of a vernier callipers" has n divisions/cm. n divisions of the vernier scale coincide with ( n − 1 ) divisions of main scale. The least count of the vernier callipers is (a) 1 (n+1)(n−1) cm (b) 1 n cm (c) 1 n2 cm (d) 1 n(n+1) cm (Odisha NEET 2019) 10. A student measured the diameter of a small steel ball using a screw gauge of least count 0.001 cm . The main scale reading is 5 mm and zero of circular scale division coincides with 25 divisions above the reference level. If screw gauge has a zero error of - 0.004 cm , the correct diameter of the ball is (a) 0.521 cm (b) 0.525 cm
(c) 0.053 cm (d) 0.529 cm (2018) 11. In an experiment, four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows P = a 3b 2 cd . % error in P is (a) 7% (b) 4% (c) 14% (d) 10% (2013) 12. A student measures the distance traversed in free fall of a body, initially at rest, in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of . the distance and the time are e1 and e2 respectively, the percentage error in the estimation of g is (a) e2 − e1 (b) e1 + 2e2 (c) e1 + e2 (d) e1 − 2e2 (Mains 2010) 13. If the error in the measurement of radius of a sphere is 2%, then the error in the determination of volume of the sphere will be (a) 8% (b) 2% (c) 4% (d) 6% (2008) 14. The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and lengths are 3% and 2% respectively, the maximum error in the measurement of density would be (a) 12% (b) 14% (c) 7% (d) 9% (1996) 15. Percentage errors in the measurement of mass and speed are 2% and 3% respectively. The error in the estimate of kinetic energy obtained by measuring mass and speed will be (a) 8% (b) 2% (c) 12% (d) 10%. (1995) 16. A certain body weighs 22.42 g and has a measured volume of 4.7 cc . The possible error in the measurement of mass and volume are 0.01 g and 0.1 cc . Then maximum error in the density will be (a) 22% (b) 2% (c) 0.2% (d) 0.02%. (1991) 1.3 Significant Figures 17. The area of a rectangular field (in m2 ) of length 55.3 m and breadth 25 m after rounding off the value for correct significant digit is : (a) 138 × 101 (b) 1382 (c) 1382.5 (d) 14 × 102 (2022) 18. Taking into account of the significant figures, what is the value of 9.99 m − 0.0099 m ? (a) 9.9801 m (b) 9.98 m (c) 9.980 m (d) 9.9 m (2020) 1.4 Dimensions of Physical Quantities 19. The dimensions [MLT−2 A −2 ] belong to the : (a) magnetic flux (b) self inductance (c) magnetic permeability (d) electric permittivity (2022) 20. Plane angle and solid angle have (a) Units but no dimensions (b) Dimensions but no units (c) No units and no dimensions (d) Both units and dimensions (2022) 21. If E and G respectively denote energy and gravitational constant, then E G has the dimensions of (a) [M2 ][L −2 ][T −1 ] (b) [M2 ][L −1 ][T 0 ] (c) [M][L −1 ][T −1 ]
(d) [M][L 0 ][T 0 ] (2021) 22. Dimensions of stress are (a) [MLT−2 ] (b) [ML2 T −2 ] (c) [ML0 T −2 ] (d) [ML−1 T −2 ] (2020) 23. The pair of quantities having same dimensions is (a) Impulse and Surface Tension (b) Angular momentum and Work (c) Work and Torque (d) Young's modulus and Energy (Karnataka NEET 2013) 24. The dimensions of (μ0ε0 ) −1/2 are (a) [L 1/2 T −1/2 ] (b) [L −1 T] (c) [LT−1 ] (d) [L 1/2 T 1/2 ] (Mains 2012, 2011) 25. The dimension of 1 2 ε0E 2 , where ε0 is permittivity of free space and E is electric field, is (a) ML2 T −2 (b) ML−1 T −2 (c) ML2 T −1 (d) MLT−1 (2010) 26. If the dimensions of a physical quantity are given by MaL bT c , then the physical quantity will be (a) velocity if a = 1, b = 0, c = −1 (b) acceleration if a = 1, b = 1, c = −2 (c) force if a = 0, b = −1, c = −2 (d) pressure if a = 1, b = −1, c = −2 (2009) 27. Which two of the following five physical parameters have the same dimensions? 1.energy density 2.refractive index 3.dielectric constant 4.Young's modulus 5.magnetic field (2008) (a) 1 and 4 (b) 1 and 5 (c) 2 and 4 (d) 3 and 5 28. Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and of current I , would be (a) [ML2 T −2 ] (b) [ML2 T −1 I −1 ] (c) [ML2 T −3 I −2 ] (d) [ML2 T −3 I −1 ] (2007) 29. The ratio of the dimensions of Planck's constant and that of moment of inertia is the dimensions of (a) time (b) frequency (c) angular momentum (d) velocity. (2005) 30. The dimensions of universal gravitational constant are (a) [M−1 L 3 T −2 ] (b) [ML2 T −1 ] (c) [M−2 L 3 T −2 ] (d) [M−2 L 2 T −1 ] (2004,1992) 31. The dimensions of Planck's constant equals to that of (a) energy (b) momentum (c) angular momentum (d) power. (2001) 32. Which pair do not have equal dimensions? (a) Energy and torque (b) Force and impulse (c) Angular momentum and Planck's constant (d) Elastic modulus and pressure. (2000) 33. The dimensions of impulse are equal to that of (a) pressure (b) linear momentum (c) force (d) angular momentum (1996) 34. Which of the following dimensions will be the same as that of time? (a) L R (b) C L (c) LC
(d) R L (1996) 35. The dimensions of RC is (a) square of time (b) square of inverse time (c) time (d) inverse time. (1995) 36. Which of the following has the dimensions of pressure? (a) [MLT−2 ] (b) [ML−1 T −2 ] (c) [ML−2 T −2 ] (d) [M−1 L −1 ] (1994, 1990) 37. Of the following quantities, which one has dimensions different from the remaining three? (a) Energy per unit volume (b) Force per unit area (c) Product of voltage and charge per unit volume (d) Angular momentum. (1989) 1.5 Dimensional Formulae and Dimensional Equations 38. The dimensional formula of magnetic flux is (a) [M0 L −2 T −2 A −2 ] (b) ML 0 T −2 A −2 ] (c) [ML2 T −2 A −1 ] (d) [ML2 T −1 A 3 ] (1999) 39. The dimensional formula of permeability of free space μ0 is (a) [MLT−2 A −2 ] (b) [M0 L 1 T] (c) [M0 L 2 T −1 A 2 ] (d) none of these. (1991) 40. According to Newton, the viscous force acting between liquid layers of area A and velocity gradient Δv/ΔZ is given by F = −ηA Δv ΔZ , where η is constant called coefficient of viscosity. The dimensional formula of η is (a) [ML−2 T −2 ] (b) [M0 L 0 T 0 ] (c) [ML2 T −2 ] (d) [ML−1 T −1 ]. (1990) 41. Dimensional formula of self inductance is (a) [MLT−2 A −2 ] (b) [ML2 T −1 A −2 ] (c) [ML2 T −2 A −2 ] (d) [ML2 T −2 A −1 ] (1989) 42. The dimensional formula of torque is (a) [ML2 T −2 ] (b) [MLT−2 ] (c) [ML−1 T −2 ] (d) [ML−2 T −2 ]. (1989) 43. If C and R denote capacitance and resistance, the dimensional formula of CR is (a) [M0 L 0 T 1 ] (b) [M0 L 0 T 0 ] (c) [M0 L 0 T −1 ] (d) not expressible in terms of MLT. (1988) 44. The dimensional formula of angular momentum is (a) [ML2 T −2 ] (b) [ML−2 T −1 ] (c) [MLT−1 ] (d) [ML2 T −1 ]. (1988) 1.6 Dimensional Analysis and its Applications 45. If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy. (a) [F][A −1 ][T] (b) [F][A][T] (c) [F][A][T 2 ] (d) [F][A][T −1 ] (2021) 46. A physical quantity of the dimensions of length that can be formed out of c, G and e 2 4πε0 is [ c is velocity of light, G is the universal constant of gravitation and e is charge] (a) c 2 [G e 2 4πε0 ] 1/2 (b) 1 c 2 [ e 2 G4πε0 ] 1/2 (c) 1 c G e 2 4πε0 (d) 1 c 2 [G e 2 4πε0 ] 1/2 (2017)