Physical World, Units & Measurements Biology | Chemistry | Physics | NTA Please enter your email: 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 dimensions of Planck’s constant are (a) [ML–3T–1] (b) [ML–2T–1] (c) [M0L–1T–3] (d) [ML2T–1] The dimensions of mobility are (a) M–2T2A (b) M–1T2A (c) M–2T3A (d) M–1T3A 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 Using mass (M), length (L), time (T) and current (A) as fundamental quantities, the dimensions of permeability are (a) [M–1LT–2A] (b) [ML–2T–2A–1] (c) [MLT–2A–2] (d) [MLT–1A–1] The dimensions of energy are (a) [ML3T–3] (b) [ML–1T–1] (c) [ML2T–2] (d) [MT–2] 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 What is the fractional error in g calculated from T = 2π √l/ g? Given fraction errors in T and l are ± x and ± y respectively? (a) x + y (b) x – y (c) 2x + y (d) 2x – y 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 % 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 Parsec is the unit of (a) time (b) distance (c) frequency (d) angular acceleration 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 The least count of a stop watch is 0.2 second. The time of 20 oscillations of a pendulum is measured to be 25 second. The percentage error in the measurement of time will be (a) 8% (b) 1.8% (c) 0.8% (d) 0.1% The dimensions of Wien’s constant are (a) [ML0TK] (b) [M0LT0K] (c) [M0L0TK] (d) [MLTK] Dimensions of coefficient of viscosity is (a) [MT2] (b) [ML–3T–4] (c) [ML–1T–2] (d) [ML–1T–1] The dimensional formula for magnetic flux is (a) [ML2T–2A–1] (b) [ML3T–2A–2] (c) [M0L–2T2A–2] (d) [ML2T–1A2] Velocity of light is equal to (a) √(1 /ε0μ0) (b) √(ε0 / μ0) (c) ε0 / μ0 (d) ε0μ If E, m, J and G represent energy, mass, angular momentum and gravitational constant respectively, then the dimensional formula of EJ2/m5G2 is same as that of the (a) angle (b) length (c) mass (d) time The physical quantity which has the dimensional formula [M1T-3] is (a) surface tension (b) solar constant (c) density (d) compressibility 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 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 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 is a dimensional constant? (a) Refractive index (b) Poissons ratio (c) Strain (d) Gravitational constant 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 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 physical quantities not having same dimensions are (a) torque and work (b) momentum and Planck’s constant (c) stress and Young’s modulus (d) speed 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 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 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] 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) Dimensions of electrical resistance are (a) [ML2T–3A–1] (b) [ML2T–3A–2] (c) [ML3T–3A–2] (d) [ML–1L3T3A2] Which of the following pairs does not have similar dimensions? (a) tension and surface tension (b) stress and pressure (c) Planck’s constant and angular momentum (d) angle and strain The dimensional formula of magnetic flux is (a) [ML0T–2A–1] (b) [ML2T–2A–1] (c) [ML2T–1A3] (d) [M0L–2T–2A–2] The dimensional formula for torque is (a) ML2T–2 (b) ML–1T–1 (c) L2T–1 (d) M2T–2K–1 The dimensions of 1/εo e2/hc are (a) M-1 L-3 T4 A2 (b) ML3 T-4 A-2 (c) M0 L0 T0 A0 (d) M-1 L-3 T2 A 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 The dimensional formula of farad is (a) [M–1L–2TQ] (b) [M–1L–2T2Q2] (c) [M–1L–2TQ2 ] (d) [M–1L–2T2Q] If the error in the measurement of the volume of sphere is 6%, then the error in the measurement of its surface area will be (a) 2% (b) 3% (c) 4% (d) 7.5% 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 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] 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] 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 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 ] 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 Loading … Question 1 of 45
