Embibe Experts Solutions for Chapter: Physical World and Measurement, Exercise 1: JEE Advanced Paper 2 - 2016

A physical quantity $\overrightarrow{S}$ is defined as $\overrightarrow{S}=\frac{\left(\overrightarrow{E}\times \overrightarrow{B}\right)}{{\mu }_0}$. where $\overrightarrow{E}$ is electric field, $\overrightarrow{B}$ is magnetic field and ${\mu }_0$ is the permeability of free space. The dimensions of $\overrightarrow{S}$ are the same as the dimensions of which of the following quantity/quantities?

A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is $\delta T=0.01 \mathrm{s}$ and he measures the depth of the well to be $L=20$ meters. Take the acceleration due to gravity $g=10 \mathrm{m} {\mathrm{s}}^{-2}$ and the velocity of sound is $300 \mathrm{m} {\mathrm{s}}^{-1}$. Then the fractional error in the measurement, $\frac{\delta L}{L}$ is closest to

In an experiment to determine the acceleration due to gravity $g$, the formula used for the time period of a periodic motion is $T=2\pi \sqrt{\frac{7\left(R-r\right)}{5g}}.$ The values of $R$ and $r$ are measured to be $\left(60\pm 1\right) \mathrm{mm} \text{and} \left(10\pm 1\right) \mathrm{mm},$ respectively. In five successive measurements, the time period is found to be $0.52 \mathrm{s}$, $0.56 \mathrm{s}$, $0.57 \mathrm{s}$, $0.54 \mathrm{s}$ and $0.59 \mathrm{s}$. The least count of the watch used for the measurement of time period is $0.01 \mathrm{s}$. Which of the following statements (s) is (are) true?

In terms of potential difference $V$ , electic current $I$ , permittivity ${\epsilon }_0$ , permeability ${\mu }_0$ and speed of light $c$ , the dimensionally correct equation(s) is (are)

Sometimes it is convenient to construct a system of units so that all quantities can be expressed in terms of only one physical quantity. In one such system, dimensions of different quantities are given in terms of a quantity $X$ as follows: $\left[\mathrm{position}\right]=\left[X^{\alpha }\right];$ $\left[\mathrm{speed}\right]=\left[X^{\beta }\right]$; $\left[\mathrm{acceleration}\right]=\left[X^p\right]$;$\left[\mathrm{linear}\mathrm{momentum}\right]=\left[X^q\right]$; $\left[\mathrm{force}\right]=\left[X^r\right]$. Then

Let us consider a system of units in which mass and angular momentum are dimensionless. If the length has a dimension of $\mathrm{L},$ which of the following statement (s) is/are correct?

A length - scale $\left(l\right)$ depends on the permittivity $\left(\mathrm{\epsilon }\right)$ 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 expressions (s) for $l$ is (are) dimensionally correct?

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