Units, Dimensions & Measurements PYQs Set 9 (PDF)

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Set 9 of 10 · Questions 241-270 of 294

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Mere Teacher · Previous Year Questions JEE Main Physics · Units, Dimensions & Measurements · Set 9 (Q241-270)
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241. $Dimension of \frac{1}{μ _{0} ϵ _{0}} should be equal to$ (1) $L T^{- 1}$ (2) $T^{2} L^{- 2}$ (3) $L^{2} T^{- 2}$ (4) $T L^{- 1}$ 242. $If momentum [P], area [A] and time [T] are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is :$ (1) $[P A^{- 1} T°]$ (2) $[P A T^{- 1}]$ (3) $[P A^{- 1} T]$ (4) $[P A^{- 1} T^{- 1}]$ 243. $Match List I with List II LIST I A. Planck’s constant (h) B. Stopping potential (Vs) C. Work function (^{φ}) D. Momentum (p) LIST II I. [M^{1} L^{2} T^{- 2}] II. [M^{1} L^{1} T^{- 1}] III. [M^{1} L^{2} T^{- 1}] IV [M^{1} L^{2} T^{- 3} A^{- 1}]$ (1) $A-III,B-I, C-II,D-IV$ (2) $A-III, B-IV, C-I, D-II$ (3) $A-II, B-IV, C-III, D-I$ (4) $A-I, B-III, C-IV, D-II$ 244. $The density of a material in SI units is 128 k g m^{-3} . In certain units in which the units of length is 25 cm and the unit of mass is 50 g, the numerical value of density of the material is :$ (1) $410$ (2) $40$ (3) $640$ (4) $16$ 245. $Match List Ι with List ΙΙ and select the correct answer using the codes given below the lists : List Ι List ΙΙ P. Boltzmann constant 1. [M L^{2} T^{-1}] Q. Coefficient of viscosity 2. [M L^{-1} T^{-1}] R. Planck constant 3. [M L T^{-3} K^{-1}] S. Thermal conductivity 4. [M L^{2} T^{-2} K^{-1}] Codes : P Q R S$ (1) $3 1 2 4$ (2) $3 2 1 4$ (3) $4 2 1 3$ (4) $4 1 2 3$ 246. $If A = 3 i - 2 j + k, B = i - 3 j + 5 k and C = 2 i + j - 4 k form a right angled triangle. Then out of the following which one is satisfied?$ (1) $A=B+C and A^{2} = B^{2} + C^{2}$ (2) $A=B+C and B^{2} = A^{2} + C^{2}$ (3) $B=A+C and B^{2} = A^{2} + C^{2}$ (4) $B=A+C and A^{2} = B^{2} + C^{2}$ 247. $Match List I with List II List-I A. Surface tension B. Pressure C. Viscosity D. Impulse List-II I. Kg m^{- 1} s^{- 1} II. Kg m s^{- 1} III. Kg m^{- 1} s^{- 2} IV. Kg s^{- 2} Choose the correct answer from the options given below:$ (1) $A-IV, B-III,C-II, D-I$ (2) $A-IV, B-III, C-I, D-II$ (3) $A-III, B-IV, C-I, D-II$ (4) $A-II, B-I, C-III, D-IV$ 248. $Velocities (V) and accelerations (a) in two systems of units 1 and 2 are related as V_{2} = \frac{n}{m ^{2}} V_{1} and a_{2} = \frac{a _{1}}{mn} respectively. Here m and n are constants. Dimensionally relations between distances (S_{1} and S_{2}) and times (t_{1} and t_{2}) in the two systems are respectively.$ (1) $S_{2} = (\frac{n}{m})^{3} S_{1} and t_{2} = \frac{n ^{2}}{m} t_{1}$ (2) $S_{2} = (\frac{n}{m})^{3} S_{1} and t_{2} = \frac{m}{n ^{2}} t_{1}$ (3) $S_{2} = \frac{m}{n ^{2}} S_{1} and t_{2} = \frac{m ^{2}}{n ^{4}} t_{1}$ (4) $S_{2} = \frac{n ^{2}}{m} S_{1} and t_{2} = \frac{m ^{2}}{n ^{4}} t_{1}$ 249. $If dimensions of critical velocity v_{c} of a liquid flowing through a tube are expressed as [η^{x} ρ^{y} r^{z}] where η, ρ and r are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively then the values of x, y and z are given by$ (1) $- 1, - 1, - 1$ (2) $1, 1, 1$ (3) $1, - 1, - 1$ 250. $Two protons are kept at a separation of 40Å . F_{n} is the nuclear force and F_{e} is the electrostatic force between them. Then$ (1) $F_{n} ≪ F_{e}$ (2) $F_{n} \approx F_{e}$ (3) $F_{n} ≫ F_{e}$ (4) $F_{n} = F_{e}$ 251. $The quantities x = \frac{1}{μ _{0} ϵ _{0}}, y = \frac{E}{B} and z = \frac{l}{C R} are defined where C -capacitance, R -Resistance, l length, E -Electric field, B -magnetic field and ϵ_{0}, μ_{0} - free space permittivity and permeability respectively. Then$ (1) $Only x and y have the same dimension$ (2) $Only x and z have the same dimension$ (3) $x, y and z have the same dimension$ (4) $Only y and z have the same dimension$ 252. $The dimensions of (μ_{0} ϵ_{0})^{- 1/2} are$ (1) $[L^{1/2} T^{- 1/2}]$ (2) $[L2T]$ (3) $[L T^{- 1}]$ (4) $[L^{1/2} T^{1/2}]$ 253. $Dimensions of gyromagnetic ratio are$ (1) $(L^{1} M^{0} T^{1} I^{1})$ (2) $(L^{1} M^{0} I^{0} T^{- 1})$ (3) $(L^{0} M^{- 1} T^{1} I^{1})$ (4) $(L^{- 1} M^{0} T^{1} I^{1})$ 254. $The dimensional formula of torque is$ (1) $[M L^{2} T^{- 2}]$ (2) $[ML T^{- 2}]$ (3) $[M L^{- 1} T^{- 2}]$ (4) $[M L^{- 2} T^{- 2}]$ 255. $Dimensions of stress are [NEET 2020]$ (1) $M L^{2} T^{- 2}$ (2) $M L^{0} T^{- 2}$ (3) $M L^{- 1} T^{- 2}$ (4) $M L T^{- 2}$ 256. $The unit of magnetic induction is$ (1) $Wb m^{- 2}$ (2) $Wb m^{- 1}$ (3) $WbA$ (4) $Wb$ 257. $In a Vernier Calipers. 10 divisions of Vernier scale is equal to the 9 divisions of main scale. When both jaws of Vernier calipers touch each other, the zero of the Vernier scale is shifted to the left of zero of the main scale and 4^{t h} Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to 1 mm. While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between 30 and 31 divisions of main scale reading and 6^{t h} Vernier scale division exactly, coincides with the main scale reading. The diameter of the spherical body will be:$ (1) $3.02 cm$ (2) $3.06 cm$ (3) $3.10 cm$ (4) $3.20 cm$ 258. $When both jaws of vernier callipers touch each other, zero mark of the vernier scale is right to zero mark of main scale, 4^{th} mark on vernier scale coincides with certain mark on the main scale. While measuring the length of a cylinder, observer observes 15 divisions on main scale and 5^{th} division of vernier scale coincides with a main scale division. Measured length of cylinder is____mm. (Least count of Vernier calliper = 0.1 mm)$ (1) $15.5$ (2) $15.9$ (3) $15.1$ (4) $15.4$ 259. $The dimensions of RC is$ (1) $square of time$ (2) $square of inverse time$ (3) $time$ (4) $inverse time.$ 260. $Match the physical quantities given in List-I with dimensions in List-II. List I A. Gravitational constant B. Stefan’s constant C. Permitivity D. Specific heat capacity List II (i) (M^{0} L^{2} T^{- 2} K^{- 1}) (ii) (M^{- 1} L^{3} T^{- 2}) (iii) (ML^{0} T^{- 3} K^{- 4}) (iv) (M^{- 1} L^{- 3} T^{4} I^{2}) (The dimension of mass, length, time, temperature and current are M, L, T, K and I, respectively). The correct match is A B C D$ (1) $IV I III II$ (2) $I IV II III$ (3) $III II I IV$ (4) $II III IV I$ 261. $A student determined Young's Modulus of elasticity using the formula The value of g is taken to be 9.8m/, without any significant error, his observation are as following. Physical Quantity Least count of the Equipment used for measurement Observed value Mass(M) 1 g 2 kg Length of bar(L) 1 mm 1 m Breadth of bar(b) 0.1 mm 4 cm Thickness of bar(d) 0.01 mm 0.4 cm Depression(8) 0.01 mm 5 mm Then the fractional error in the measurement Y of is:$ (1) $0.0083$ (2) $0.0155$ (3) $0.155$ (4) $0.083$ 262. $The least count of the main scale of a vernier callipers is 1 mm . Its vernier scale is divided into 10 divisions and coincide with 9 divisions of the main scale. When jaws are touching each other, the 7^{th} division of vernier scale coincides with a division of main scale and the zero of vernier scale is lying right side of the zero of main scale. When this vernier is used to measure length of a cylinder the zero of the vernier scale between 3.1 cm and 3.2 cm and 4^{th} VSD coincides with a main scale division. The length of the cylinder is (VSD is vernier scale division)$ (1) $3.21 cm$ (2) $2.99 cm$ (3) $3.07 cm$ (4) $3.2 cm$ 263. $Match List I with List II: List-I (Physical Quantity) A. Pressure gradient B. Energy density C. Electric Field D. Latent heat List-II (Dimensional Formula) I. [M^{0} L^{2} T^{- 2}] II. [M^{1} L^{- 1} T^{- 2}] III. [M^{1} L^{- 2} T^{- 2}] IV. [M^{1} L^{1} T^{- 3} A^{- 1}] Choose the correct answer from the options given below:$ (1) $A-III,B-II,C-I,D-IV$ (2) $A-II, B-III, C-IV, D-I$ (3) $A-III, B-II, C-IV, D-I$ (4) $A-II, B-III, C-I, D-IV$ 264. $A physical quantity 'y' is represented by the formula y = m^{2} r^{- 4} g^{x} l^{- \frac{3}{2}} If the percentage errors found in y,m,r,l and g are18,1,0,5,4 and p respectively, then find the value of x and p.$ (1) $5 and \pm 2$ (2) $4 and \pm 3$ (3) $\frac{16}{3} and \pm \frac{3}{2}$ (4) $8 and \pm 2$ 265. $Unit of pole strength of a magnet is$ (1) $Am^{- 1}$ (2) $Am^{2}$ (3) $Am^{- 2}$ (4) $Am$ 266. $Statement : 1 If three forces F_{1}, F_{2} and F_{3} are represented by three sides of a triangle and F_{1} + F_{2} = - F_{3}, then these three forces are concurrent forces and satisfy the condition for equilibrium. Statement : II A triangle made up of three forces F_{1}, F_{2} and F_{3} as its sides taken in the same order, satisfy the condition for translatory equilibrium. choose the most appropriate answer from the options given below:$ (1) $Statement-I is false but Statement-II is true$ (2) $Statement-I is true but Statement-II is false$ (3) $Both Statement-I and Statement-II are false$ (4) $Both Statement-I and Statement-II are true.$ 267. $The SI unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be$ (1) $[M L^{- 1} T^{- 1}]$ (2) $[M L^{- 1} T^{- 2}]$ (3) $[M L^{2} T^{- 1}]$ (4) $[M^{- 1} L^{3} T^{0}]$ 268. $The dimension of mutual inductance is :$ (1) $[M L^{2} T^{- 2} A^{- 1}]$ (2) $[M L^{2} T^{- 3} A^{- 1}]$ (3) $[M L^{2} T^{- 2} A^{- 2}]$ (4) $[M L^{2} T^{- 3} A^{- 2}]$ 269. $The diameter of a spherical bob is measured using a vernier callipers. 9 divisions of the main scale, in the vernier callipers, are equal to 10 divisions of vernier scale. One main scale division is 1mm. The main scale reading 10 mm is and 8^{t h} division of vernier scale was found to coincide exactly with one of the main scale division. If the given vernier callipers has positive zero error of 0.04cm, then the radius of the bob is ..... x 1 0^{- 2} cm.$ 270. $In a screw gauge, there are 100 divisions on the circular scale and the main scale moves by 0.5 mm on a complete rotation of the circular scale. The zero of circular scale lies 6 divisions below the line of graduation when two studs are brought in contact with each other. When a wire is placed between the studs, 4 linear scale divisions are clearly visible while 4 6^{t h} division the circular scale coincide with the reference line. The diameter of the wire is _____ x 1 0^{- 2} mm.$