Unit 1: Physics and Measurement

A rectangular card measures 2.34 cm by 1.5 cm. Its area, written to the correct number of significant figures, is

Three lengths, 12.43 m, 1.2 m and 0.065 m, are added. The sum, written with the correct precision, is

A student finds g from g = 4π²L/T² for a simple pendulum. The length, L = 100.0 cm, is read on a scale of least count 0.1 cm. The time for 25 oscillations, 50.0 s, is read on a stopwatch of least count 0.1 s. Taking each least count as the absolute error, the maximum percentage error in g is

A quantity is found from Q = a³b²/(c√d). The percentage errors in a, b, c and d are 1%, 2%, 3% and 4%. The maximum percentage error in Q is

The period of an oscillator is timed five times: 2.04 s, 1.96 s, 2.06 s, 1.94 s and 2.00 s. Using the mean absolute error, the percentage error in the mean period is

Read the following statements about SI units. (a) The kelvin is an SI base unit. (b) The newton is an SI base unit. (c) The candela is the SI base unit of luminous intensity. (d) The ampere is the SI base unit of electric charge. (e) The mole is the SI base unit of amount of substance. How many of the above statements are correct?

Given below are two statements. Statement I: The length 0.0250 m has two significant figures. Statement II: Writing 4700 m as 4.70 × 10³ m states that the length is known to three significant figures. In the light of the above statements, choose the correct answer.

Given below are two statements: one is labelled Assertion A and the other is labelled Reason R. Assertion A: A measuring instrument with least count 0.01 cm gives more precise readings than one with least count 0.1 cm. Reason R: A smaller least count always makes a measurement more accurate. In the light of the above statements, choose the correct answer.

The radius of a ball bearing is measured as (2.50 ± 0.02) cm. The percentage error in its volume, found from V = (4/3)πr³, is

Two lengths are measured as (32.4 ± 0.1) cm and (12.4 ± 0.1) cm. The percentage error in their difference is

Two resistors, (12 ± 0.6) Ω and (6 ± 0.3) Ω, are joined in parallel. Using 1/R = 1/R₁ + 1/R₂, the equivalent resistance with its maximum absolute error is

Using E = hν, where E is the energy of a photon and ν its frequency, the dimensions of Planck's constant h are

The velocity of a particle is given by v = at + b/(t + c), where t is time and a, b and c are constants. The dimensions of ab/c are

A small liquid drop oscillates about its spherical shape. Its period T depends only on the density ρ of the liquid, the radius r of the drop and the surface tension S (dimensions [M T⁻²]). By dimensional analysis, T is proportional to

In a new system of units, the unit of mass is 2 kg, the unit of length is 5 m and the unit of time is 10 s. An energy of 1 J, expressed in this system, is

A system takes force, length and time as its base quantities, with units 100 N, 10 m and 100 s. The unit of mass in this system is

Given below are two statements: one is labelled Assertion A and the other is labelled Reason R. Assertion A: Dimensional analysis shows that v² = u² + 2as is consistent, but it cannot confirm that the factor in the last term is 2. Reason R: Pure numbers such as 2 have no dimensions. In the light of the above statements, choose the correct answer.

Given below are two statements: one is labelled Assertion A and the other is labelled Reason R. Assertion A: Because torque and work have the same dimensions, they are the same physical quantity. Reason R: Torque and work both have the dimensions [M L² T⁻²]. In the light of the above statements, choose the correct answer.

Given below are two statements. Statement I: Impulse and linear momentum have the same dimensions. Statement II: Pressure and energy per unit volume have different dimensions. In the light of the above statements, choose the correct answer.

Read the following statements about dimensions. (a) Strain is dimensionless. (b) Refractive index is dimensionless. (c) Angular velocity is dimensionless. (d) Relative density is dimensionless. (e) The coefficient of static friction is dimensionless. (f) Planck's constant is dimensionless. How many of the above statements are correct?

Coulomb's law gives the force between two point charges q in vacuum as F = q²/(4πε₀r²). Taking current, with dimension [A], as a base quantity, the dimensions of the permittivity ε₀ are

Given below are two statements. Statement I: Plane angle and solid angle both have the dimensions of length, [L]. Statement II: The light year is a unit of time. In the light of the above statements, choose the correct answer.