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Units & Dimensions — JEE Practice
46 practice questions across 3 topics. Filter by difficulty, solve topic-wise MCQs, and review detailed solutions.
3 Topics46 Questions
SI Units & Conversions(16 Qs)
easy (5)
medium (6)
Q1The dimensions of Planck's constant are:Q2If force F, length L, and time T are fundamental units, the dimensions of mass are:Q3The dimensional formula of angular momentum is:Q4Which pair has the same dimensions?Q5The number of significant figures in 0.006032 is:Q6The dimensions of permittivity of free space ε₀ are:
hard (5)
Q1In a new system of units, the unit of mass is α kg, length is β m, and time is γ s. The value of 1 J in this new system is:Q2The velocity v of waves on a string depends on tension T and linear mass density μ. Using dimensional analysis, v is proportional to:Q3Which of the following is dimensionally correct for the equation v² = u² + 2as?Q4If E, m, l, and G denote energy, mass, angular momentum, and gravitational constant, the quantity El²/m⁵G² is dimensionless. This statement is:Q5A physical quantity X is given by X = a²b³/(c·√d). The maximum percentage error in X is (given % errors in a, b, c, d are 1%, 2%, 3%, 4%):
Dimensional Analysis(15 Qs)
easy (5)
medium (5)
Q1Using dimensional analysis, the time period T of a simple pendulum depends on length l and acceleration g as:Q2The dimension of 1/(μ₀ε₀) is:Q3The principle of homogeneity of dimensions states that:Q4A quantity has the dimensions [ML⁻¹T⁻²]. It could be:Q5If velocity (v), force (F), and energy (E) are taken as fundamental quantities, the dimension of mass in this system is:
hard (5)
Q1The equation P = (a-t²)/(bx), where P is pressure, t is time, and x is distance. The dimensions of a/b are:Q2Stokes' law gives viscous force F = 6πηrv. Using this, the dimension of viscosity η is:Q3The van der Waals equation is (P + a/V²)(V - b) = RT. The dimensions of a are:Q4Using dimensional analysis, the expression for viscous force cannot be derived because:Q5The expression for energy stored in an inductor is ½LI². The dimension [ML²T⁻²A⁻²] represents:
Errors & Measurements(15 Qs)
easy (5)
Q1The least count of a vernier caliper with 1 MSD = 1 mm and 50 VSD = 49 MSD is:Q2The error in measurement of radius is 2%. The error in the calculated area of a circle is:Q3Systematic errors can be removed by:Q4If a screw gauge has a pitch of 0.5 mm and 50 divisions on the circular scale, its least count is:Q5Random errors can be minimised by:
medium (5)
Q1The density of a cube is measured using mass and length. If mass has 1% error and length has 2% error, the maximum % error in density is:Q2In an experiment, refractive index is measured as n = real depth/apparent depth. If real depth = 12.0 ± 0.1 cm and apparent depth = 9.0 ± 0.1 cm, the % error in n is:Q3The resistance R = V/I where V = 100 ± 5 V and I = 10 ± 0.2 A. The percentage error in R is:Q4Zero error in a screw gauge is +0.004 cm. The actual reading when the observed reading is 2.546 cm:Q5A physical quantity Q = A²B³/(C⁴√D). The % error in Q if % errors in A, B, C, D are 1%, 2%, 3%, 4% respectively:
hard (5)
Q1In a Wheatstone bridge, resistances P = 100 ± 1 Ω, Q = 10 ± 0.5 Ω, R = 50 Ω. At balance, S = ?. The maximum possible error in S is:Q2The period of oscillation T of a loaded spring is T = 2π√(m/k). The errors in m and k are 2% and 4%. The % error in T is:Q3In an experiment, time for 20 oscillations is measured as 40 ± 1 s with a stopwatch of least count 1 s. The % error in measurement of g using T = 2π√(l/g) with l measured to 1% accuracy is approximately:Q4The pitch of a screw gauge is found to be 1.5 mm using a scale of least count 0.5 mm. The circular scale has 150 divisions. A wire diameter measured as 3 divisions on main scale + 78 on circular scale with +3 divisions zero error. The corrected diameter is:Q5The measured values of a quantity are 2.34, 2.36, 2.35, 2.37, 2.33. The mean absolute error is:
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