NCERT Solutions

The length, breadth and thickness of a rectangular sheet of metal are $4.234 \text{ m}, 1.005 \text{ m}$, and 2.01 cm respectively. Give the area and volume of the sheet to correct significant figures.

A famous relation in physics relates 'moving mass' $m$ to the 'rest mass' $m_{o}$ of a particle in terms of its speed $v$ and the speed of light, $c$. (This relation first arose as a consequence of special relativity due to Albert Einstein). A boy recalls the relation almost correctly but forgets where to put the constant c. He writes : $m = \frac{m_{O}}{(1-v^{2})^{1 / 2}}$. Guess where to put the missing $c$.

The unit of length convenient on the atomic scale is known as an angstrom and is denoted by $\AA: 1 \AA = 10^{-10} \text{ m}$. The size of a hydrogen atom is about $0.5 \AA$. What is the total atomic volume in $\text{m}^3$ of a mole of hydrogen atoms ?

One mole of an ideal gas at standard temperature and pressure occupies 22.4 L (molar volume). What is the ratio of molar volume to the atomic volume of a mole of hydrogen ? (Take the size of hydrogen molecule to be about $1 \AA$). Why is this ratio so large ?

Explain this common observation clearly : If you look out of the window of a fast moving train, the nearby trees, houses etc. seem to move rapidly in a direction opposite to the train's motion, but the distant objects (hill tops, the Moon, the stars etc.) seem to be stationary. (In fact, since you are aware that you are moving, these distant objects seem to move with you).

The Sun is a hot plasma (ionized matter) with its inner core at a temperature exceeding $10^{7} \text{ K}$, and its outer surface at a temperature of about 6000 K . At these high temperatures, no substance remains in a solid or liquid phase. In what range do you expect the mass density of the Sun to be, in the range of densities of solids and liquids or gases? Check if your guess is correct from the following data: mass of the Sun $= 2.0 \times 10^{30} \text{ kg}$, radius of the Sun $= 7.0 \times 10^{8} \text{ m}$.

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

A new unit of length is chosen such 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 min and 20 s to cover this distance?

A student measures the thickness of a human hair by looking at it through a microscope of magnification 100. He makes 20 observations and finds that the average width of the hair in the field of view of the microscope is 3.5 mm. What is the estimate on the thickness of hair ?

The photograph of a house occupies an area of $1.75 \text{ cm}^2$ on a 35 mm slide. The slide is projected on to a screen, and the area of the house on the screen is $1.55 \text{ m}^2$. What is the linear magnification of the projector-screen arrangement.