Question 1 of 17 How many centimeters are there in one Fermi A [latex]10^{-10}[/latex] B [latex]10^{-13}[/latex] C [latex]10^{-1}[/latex] D [latex]10^{-18}[/latex] 💡 Explanation [latex]1 \text{ Fermi} = 10^{-15}\text{ m} = 10^{-15} \times 100\text{ cm} = 10^{-13}\text{ cm}[/latex] Question 2 of 17 The proportionality constant A always has dimension B never have dimension C may have dimension D none of these 💡 Explanation Whether a proportionality constant has dimensions depends on the physical relation it connects. For example, in [latex]F = ma[/latex], the constant of proportionality is dimensionless, but in [latex]F = G\dfrac{m_1 m_2}{d^2}[/latex], the constant G has dimensions. Hence, it "may" have dimension depending on the equation. Question 3 of 17 Which of the following will have same dimension A work and torque B momentum and moment C stress and strain D elasticity and strain 💡 Explanation [latex]\text{Work} = F \times d = [MLT^{-2}][L] = [ML^2T^{-2}][/latex] [latex]\text{Torque} = F \times d = [MLT^{-2}][L] = [ML^2T^{-2}][/latex] Both have the same dimension [latex][ML^2T^{-2}][/latex], even though they are physically different quantities (work is scalar, torque is a vector/pseudo-vector). Question 4 of 17 Dimension of angular speed (𝜔) is A [latex][M^0LT^{-1}][/latex] B [latex][M^0L^0T^{-2}][/latex] C [latex][M^0LT][/latex] D [latex][M^0L^0T^{-1}][/latex] 💡 Explanation [latex]\omega = \frac{\theta}{t}[/latex] Angle 𝜃 (arc/radius) is dimensionless [latex][M^0L^0T^0][/latex], so: [latex][\omega] = \frac{[M^0L^0T^0]}{[T]} = [M^0L^0T^{-1}][/latex] Question 5 of 17 The gravitational force between two bodies of mass 𝑚1 and 𝑚2, separated by distance d is given by [latex]F = G\dfrac{m_1 m_2}{d^2}[/latex], where G is gravitational constant. The dimension of G is A [latex][M^{-1}L^3T^{-1}][/latex] B [latex][M^{-1}L^3T^{-2}][/latex] C [latex][M^{-1}L^{-1}T^{-2}][/latex] D dimension less 💡 Explanation [latex]G = \frac{Fd^2}{m_1 m_2} = \frac{[MLT^{-2}][L^2]}{[M^2]} = [M^{-1}L^3T^{-2}][/latex] Question 6 of 17 Which of the following is dimension less number A frequency B power of lens C strain D none of above 💡 Explanation Strain is defined as [latex]\dfrac{\text{change in dimension}}{\text{original dimension}}[/latex], i.e. ratio of two similar quantities (both lengths, or both volumes), so all dimensions cancel out, making it dimensionless. Frequency has dimension [latex][T^{-1}][/latex] and power of a lens has dimension [latex][L^{-1}][/latex]. Question 7 of 17 Dimensional formula of electric charge is A [C] B [latex][AT^{-1}][/latex] C [AT] D [latex][A^{-1}T^1][/latex] 💡 Explanation [latex]Q = I \times t \implies [Q] = [A][T] = [AT][/latex] Question 8 of 17 Dimensional formula of capacitance (C) is A [latex][M^{-1}L^{-2}T^4A^2][/latex] B [latex][ML^{-2}AT^2][/latex] C [latex][ML^{-2}A^{-1}T^{-2}][/latex] D [latex][ML^2A^{-1}T^{-2}][/latex] 💡 Explanation Capacitance [latex]C = \dfrac{Q}{V}[/latex], where [latex]Q = [AT][/latex] and potential [latex]V = \dfrac{\text{Work}}{\text{Charge}} = \dfrac{[ML^2T^{-2}]}{[AT]} = [ML^2T^{-3}A^{-1}][/latex] Question 9 of 17 Dimension of Planck's constant (h) is A [latex][ML^2T^{-2}][/latex] B [latex][MLT^{-1}][/latex] C [latex][ML^2T^{-1}][/latex] D none of above 💡 Explanation From [latex]E = h\nu[/latex], [latex]h = \frac{E}{\nu} = \frac{[ML^2T^{-2}]}{[T^{-1}]} = [ML^2T^{-1}][/latex] Question 10 of 17 SI unit of molar heat capacity is A [latex]JKmol^{-1}[/latex] B [latex]JK\ mole[/latex] C [latex]JK^{-1}mol[/latex] D [latex]JK^{-1}mol^{-1}[/latex] 💡 Explanation Molar heat capacity is heat required per unit mole per unit rise in temperature: [latex]C_m = \frac{Q}{n\Delta T}[/latex] SI unit: [latex]\dfrac{J}{mol \cdot K} = JK^{-1}mol^{-1}[/latex] Question 11 of 17 Which of the following is the unit of magnetic permeability? A [latex]JT^{-1}[/latex] B [latex]Hm[/latex] C [latex]Hm^{-1}[/latex] D [latex]Am[/latex] 💡 Explanation The permeability of free space [latex]\mu_0[/latex] appears in the formula for magnetic field, e.g. inside a solenoid: [latex]B = \mu_0 n I[/latex]. Its SI unit is henry per metre, i.e. [latex]Hm^{-1}[/latex] (equivalently [latex]TmA^{-1}[/latex]). Question 12 of 17 Which of the following is the unit of LC, where L = inductance and C = Capacitance A [latex]s[/latex] B [latex]s^2[/latex] C [latex]s^{-1}[/latex] D [latex]s^{-2}[/latex] 💡 Explanation The angular frequency of an LC circuit is given by: [latex]\omega = \frac{1}{\sqrt{LC}}[/latex] Since [latex]\omega[/latex] has unit [latex]s^{-1}[/latex]: [latex]\sqrt{LC} = \frac{1}{\omega} \implies [\sqrt{LC}] = s \implies [LC] = s^2[/latex] Question 13 of 17 Which of the following is dimensionally incorrect? A s=ut+at² B s=ut−½at² C s=ut+5at² D s=ut+½at 💡 Explanation For dimensional correctness, every term in an equation must have the same dimensions. Here, [latex][ut]=[LT^{-1}][T]=[L][/latex], but [latex][at]=[LT^{-2}][T]=[LT^{-1}][/latex]. Since [L] ≠ [LT⁻¹], the terms ut and at cannot be added — this equation is dimensionally incorrect. (Options a, b, and c all have both terms with dimension [L], so they are dimensionally consistent, even though they may not be the standard physical equation.) Question 14 of 17 Which of the following is physically correct? A v=u+2at B v=u−½at C v=u+½at D v=at+u 💡 Explanation The standard first equation of motion is [latex]v=u+at[/latex]. Rewriting this as [latex]v=at+u[/latex] (option d) is exactly the same equation, just with terms reordered — this is the physically correct relation. Options a, b, and c all have incorrect coefficients (2, −½, and ½ respectively) in front of at. Question 15 of 17 Which of the following is the best option for a physical quantity in any two systems of units? A They have the same unit but different dimensions. B They have the same dimensions but different units. C They have the same units and the same dimensions. D They have different units and dimensions. 💡 Explanation The dimensions of a physical quantity (e.g., length = [L]) are fundamental and independent of the system of units used, but the actual unit used to express that quantity varies between systems — for example, length has dimension [L] in both SI and CGS systems, but is measured in meters (SI) versus centimeters (CGS). Question 16 of 17 Which of the following physical quantities is dimensionless? A Gravitational constant B Strain C Universal Gas constant D Stefan's constant 💡 Explanation Strain is defined as the ratio of change in dimension to the original dimension (e.g., [latex]\dfrac{\Delta L}{L}[/latex]), which is a ratio of two quantities with the same dimension, making it dimensionless. The gravitational constant, universal gas constant, and Stefan's constant all carry specific dimensional formulas. Question 17 of 17 The velocity of a particle is given in the equation [latex]v=\dfrac{b}{t}+ct^2[/latex]. What is the dimensional formula for b in the above equation? A [L] B [ML] C [T] D [MLT⁻¹] 💡 Explanation Since [latex]\dfrac{b}{t}[/latex] must have the same dimension as v, i.e., [latex][LT^{-1}][/latex]: [latex]\frac{[b]}{[T]} = [LT^{-1}] \implies [b] = [LT^{-1}]\times[T] = [L][/latex] ← Prev Check Next → Finish & See Score 0 of 17 checked ← Back 1 / 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
