Chittaranjan Dasgupta and Asok Kumar Das Solutions for Chapter: Measurement and Physics, Exercise 1: EXERCISE

A new unit of length is so chosen that the speed of light in vacuum is unity. What is the distance between the Sun and the Earth in terms of the new unit if light takes $8$minutes and $20$ seconds to cover the distance ?

A calorie is the unit of heat or energy, and it equals about $4.2 \mathrm{J}$, where $1 \mathrm{J}=1 {\mathrm{kgm}}^2{\mathrm{s}}^{-2}$. Suppose we employ a system of units in which the unit of mass equals $\alpha \mathrm{kg}$, the unit of length $\beta \mathrm{m}$, the unit of time equals $\gamma \mathrm{s}$. Show that a calorie has a magnitude $4.2 {\alpha }^{-1}{\beta }^{-2}{\gamma }^2$ in terms of the new units.

State the number of significant figures in $0.007 {\mathrm{m}}^2$.

State the number of significant digits in $2.64\times {10}^{24} \mathrm{kg}$.

State the number of significant digits in $0.2370 {\mathrm{gcm}}^{-3}$.

State the number of significant digits in $6.320 \mathrm{J}$.

Young's modulus of steel is $19\times {10}^{10} \mathrm{N}/{\mathrm{m}}^2$. Express it in CGS system of unit $\mathrm{dyne}/{\mathrm{cm}}^2$.

Round off the following numbers as directed : $5.732$ to $2$ digits.