MCQs (One or More Correct Option): Units and Measurements | JEE Advanced

The dimensions of the quantities in one (or more) of the following pairs are the same. Identify the pair (s)

The pairs of physical quantities that have the same dimensions is (are) :

The SI unit of inductance, the henry can be written as

Let [ε₀] denote the dimensional formula of the permittivity of the  vacuum, and [μ₀] that of the permeability of the vacuum. If M = mass, L = length,  T = time and I = electric current,

A student uses a simple pendulum of exactly 1m length to determine g, the acceleration due to gravity. He uses a stop watch with the least count of 1 sec for this and records 40 seconds for 20 oscillations. For this observation, which of the following statement(s) is (are) true?

Using the expression 2d sin θ = λ, one calculates the values of d by measuring the corresponding angles q in the range θ to 90°. The wavelength λ is exactly known and the error in θ is constant for all values of θ. As θ increases from 0°

Planck’s constant h, speed of light c and gravitational constant G are used to form a unit of length L and a unit of mass M. Then the correct option(s) is(are)

Consider a Vernier callipers in which each 1 cm on the main scale is divided into 8 equal divisions and a screw gauge with 100 divisions on its circular scale. In the Vernier callipers, 5 divisions of the Vernier scale coincide with 4 divisions on the main scale and in the screw gauge, one complete rotation of the circular scale moves it by two divisions on the linear scale. Then :

In terms of potential difference V, electric current I, permittivity ε₀, permeability μ₀ and speed of light c, the dimensionally correct equation(s) is(are)

A length–scale (l) depends on the permittivity (ε) of a dielectric material. Boltzmann constant (k_B), the absolute temperature (T), the number per unit volume (n) of certain charged particles, and the charge (q) carried by each of the particles. Which of the following expression(s) for I is(are) dimensionally correct?

In an experiment to determine the acceleration due to gravity g, the formula used for the time period of a periodic motion is   The values of R and r are measured to be (60 ± 1) mm and (10 ± 1) mm, respectively. In five successive measurements, the time period is found to be 0.52s, 0.56s, 0.57s, 0.54s and 0.59s. The least count of the watch used for the measurement of time period is 0.01s. Which of the following statement(s) is (are) true?