Physical World, Units & Measurements Biology | Chemistry | Physics | NTA Please enter your email: Which of the following pair of quantities do not have the same dimensions (a) Potential gradient, electric field (b) Torque, kinetic energy (c) Light year, time period (d) Impedance, reactance If L = 2.331 cm, B = 2.1 cm, then L + B = (a) 4.431 cm (b) 4.43 cm (c) 4.4 cm (d) 4 cm The physical quantity which has the dimensional formula [M1T-3] is (a) surface tension (b) solar constant (c) density (d) compressibility If the capacitance of a nanocapacitor is measured in terms of a unit ‘u‘ made by combining the electric charge ‘e‘, Bohr radius ‘ao‘, Planck’s constant ‘h‘ and speed of light ‘c‘ then (a) u=e2h/ao (b) u=hc/e2ao (c) u=e2c/hao (d) u=e2ao/hc The dimensional formula of farad is (a) [M–1L–2TQ] (b) [M–1L–2T2Q2] (c) [M–1L–2TQ2 ] (d) [M–1L–2T2Q] If Q denote the charge on the plate of a capacitor of capacitance C then the dimensional formula for Q2/C is (a) [L2M2T] (b) [LMT2] (c) [L2MT–2] (d) [L2M2T2] The dimensions of 1⁄2 ε0E2 ( ε0 : permittivity of free space, E electric field) are (a) [MLT–1] (b) [ML2T–2] (c) [ML–1T–2] (d) [ML2T–1] What is the dimensions of impedance? (a) ML2T–3I–2 (b) M–1L–2T3I2 (c) ML3T–3I–2 (d) M–1L–3T3I2 Which of the following physical quantities do not have same dimensions? (a) pressure and stress (b) tension and surface tension (c) strain and angle (d) energy and work Which of the following is a dimensional constant? (a) Refractive index (b) Poissons ratio (c) Strain (d) Gravitational constant The siemen is the SI unit of (a) resistivity (b) resistance (c) conductivity (d) conductance The speed of light (c), gravitational constant (G) and planck’s constant (h) are taken as fundamental units in a system. The dimensions of time in this new system should be (a) G1/2 h1/2 c–5/2 (b) G–1/ 2 h1/ 2 c1/ 2 (c) G1/ 2 h1/ 2 c–3/ 2 (d) G1/ 2 h1/ 2 c1/ 2 The density of material in CGS system of units is 4g/cm3. In a system of units in which unit of length is 10 cm and unit of mass is 100 g, the value of density of material will be (a) 0.4 unit (b) 40 unit (c) 400 unit (d) 0.04 unit Parsec is the unit of (a) time (b) distance (c) frequency (d) angular acceleration A force F is applied onto a square plate of side L. If the percentage error in determining L is 2% and that in F is 4%, the permissible percentage error in determining the pressure is (a) 2% (b) 4% (c) 6% (d) 8% The dimensions of energy are (a) [ML3T–3] (b) [ML–1T–1] (c) [ML2T–2] (d) [MT–2] An experiment is performed to obtain the value of acceleration due to gravity g by using a simple pendulum of length L. In this experiment time for 100 oscillations is measured by using a watch of 1 second least count and the value is 90.0 seconds. The length L is measured by using a meter scale of least count 1 mm and the value is 20.0 cm. The error in the determination of g would be: (a) 1.7% (b) 2.7% (c) 4.4% (d) 2.27% Dimensions of electrical resistance are (a) [ML2T–3A–1] (b) [ML2T–3A–2] (c) [ML3T–3A–2] (d) [ML–1L3T3A2] The length and breadth of a metal sheet are 3.124 m and 3.002 m respectively. The area of this sheet upto four correct significant figure is (a) 9.378 m2 (b) 9.37 m2 (c) 9.378248 m2 (d) 9.3782 m2 Velocity of light is equal to (a) √(1 /ε0μ0) (b) √(ε0 / μ0) (c) ε0 / μ0 (d) ε0μ The dimensional formula of the constant a in Vander Waal’s gas equation(P+a⁄V2)(V-b)=RT is (a) [ML4T–1] (b) [ML2T–2 ] (c) [ML5T–3 ] (d) [ML5T–2 ] Which two of the following five physical parameters have the same dimensions? (A) Energy density (B) Refractive index (C) Dielectric constant (D) Young’s modulus (E) Magnetic field (a) (B) and (D) (b) (C) and (E) (c) (A) and (D) (d) (A) and (E) The pressure on a square plate is measured by measuring the force on the plate and length of the sides of the plate by using the formula P = F/l2. If the maximum errors in the measurement of force and length are 4% and 2% respectively, then the maximum error in the measurement of pressure is (a) 1% (b) 2% (c) 8% (d) 10% The dimensional formula of magnetic flux is (a) [ML0T–2A–1] (b) [ML2T–2A–1] (c) [ML2T–1A3] (d) [M0L–2T–2A–2] An object is moving through the liquid. The viscous damping force acting on it is proportional to the velocity. Then dimensions of constant of proportionality are (a) [ML-1T-1] (b) [MLT-1] (c) [M0LT-1] (d) [ML0T-1] If e is the charge, V the potential difference, T the temperature, then the units of eV /T are the same as that of (a) Planck’s constant (b) Stefan’s constant (c) Boltzmann’s constant (d) gravitational constant The dimensional formula for magnetic flux is (a) [ML2T–2A–1] (b) [ML3T–2A–2] (c) [M0L–2T2A–2] (d) [ML2T–1A2] Weber is the unit of (a) magnetic susceptibility (b) intensity of magnetisation (c) magnetic flux (d) magnetic permeability The refractive index of water measured by the relation m = real depth⁄ apparent depth, is found to have values of 1.34, 1.38, 1.32 and 1.36; the mean value of refractive index with percentage error is (a) 1.35 ± 1.48 % (b) 1.35 ± 0 % (c) 1.36 ± 6 % (d) 1.36 ± 0 % Dimensions of coefficient of viscosity is (a) [MT2] (b) [ML–3T–4] (c) [ML–1T–2] (d) [ML–1T–1] Young’s modulus of a material has the same unit as that of (a) pressure (b) strain (c) compressibility (d) force The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 × 10-3 are (a) 5, 1, 2 (b) 5, 1, 5 (c) 5, 5, 2 (d) 4, 4, 2 In a vernier callipers, ten smallest divisions of the vernier scale are equal to nine smallest division on the main scale. If the smallest division on the main scale is half millimeter, then the vernier constant is (a) 0.5 mm (b) 0.1 mm (c) 0.05 mm (d) 0.005 mm Which is different from others by units? (a) Phase difference (b) Mechanical equivalent (c) Loudness of sound (d) Poisson’s ratio Multiply 107.88 by 0.610 and express the result with correct number of significant figures. (a) 65.8068 (b) 65.807 (c) 65.81 (d) 65.8 The Richardson equation is given by I=AT2e—B/kT. The dimensional formula for AB2 is same as that for (a) I T2 (b) kT (c) I k2 (d) I k2/T 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 length are 4% and 3% respectively, the maximum error in the measurement of density will be (a) 7% (b) 9% (c) 12% (d) 13% The mass of the liquid flowing per second per unit area of cross-section of the tube is proportional to (pressure difference across the ends)n and (average velocity of the liquid)n. Which of the following relations between m and n is correct? (a) m = n (b) m = – n (c) m2 = n (d) m = – n2 The dimensional formula for torque is (a) ML2T–2 (b) ML–1T–1 (c) L2T–1 (d) M2T–2K–1 The dimensions of Planck’s constant are (a) [ML–3T–1] (b) [ML–2T–1] (c) [M0L–1T–3] (d) [ML2T–1] The dimensions of Reynold’s constant are (a) [M0L0T0] (b) [ML–1T–1] (c) [ML–1T–2] (d) [ML–2T–2] Unit of magnetic moment is (a) ampere–metre2 (b) ampere–metre (c) weber–metre (d) weber/metre Using mass (M), length (L), time (T) and current (A) as fundamental quantities, the dimensional formula of permittivity is (a) [ML–2T2A] (b) [M–1L–3T4A2] (c) [MLT–2A] (d) [ML2T–1A2] The unit of impulse is the same as that of (a) energy (b) power (c) momentum (d) velocity Two quantities A and B have different dimensions which mathematical operation given below is physically meaningful? (a) A/B (b) A + B (c) A – B (d) A = B Loading … Question 1 of 45
