Q. 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).

Q. Write the dimensional formula of Force.

1. $MLT$
2. $ML{T}^2$
3. None of the above
4. $ML{T}^{-2}$

Q. The total mass of a box measured by grocer's balance is $2.300kg$. Two gold pieces of masses $20.15g$ and $20.17g$ are added to the box. What is:(a) the total mass of the box?(b) the difference in the masses of the pieces to correct significant figures?

Q. Which of the following is the most precise device for measuring length?

1. A vernier callipers with 20 divisions on the sliding scale.
2. A screw gauge of pitch 1 mm and 100 divisions on the circular scale.
3. An optical instrument that can measure length to within a wavelength of light.
   
4. All instruments have same precision.
   

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

Q. A book with many printing errors contains four different formulas for the displacement y of a particle undergoing a certain periodic motion :
(a) $y=asin{2\pi }^{t/T}$
(b) y = a sin $\upsilon$ t
(c) y = (a/T) sin t/a
(d) y = (a/$\sqrt{2}$) (sin 2$\pi$ / T + cos 2$\pi$ / T)
(a = maximum displacement of the particle, v = speed of the particle. T = time-period of motion). Rule out the wrong formulas on dimensional grounds.

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

Q. A calorie is a unit of heat or energy and it equals about $4.2J$ where $1J=1kg{m}^2{s}^{-2}$. 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.

Q. (a) The volume of a cube of side $1cm$ is equal to ________ $m^3$

Q. Fill in the blanks

Q. Answer the following:
(a) You are given a thread and a metre scale. How will you estimate the diameter of the thread?
(b) A screw gauge has a pitch of $1.0mm$ and $200$ divisions on the circular scale. Do you think it is possible to increase the accuracy of the screw gauge arbitrarily by increasing the number of divisions on the circular scale?
(c) The mean diameter of a thin brass rod is to be measured by vernier callipers. Why is a set of $100$ measurements of the diameter expected to yield a more reliable estimate than a set of $5$ measurements only?

Q. Write the number of significant digits in 6.032 ?

1. 4
2. 3
3. 2
4. none of the above

Q. 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 ?

1. 100 unit
2. 500 unit
3. 20 unit
4. 2 unit

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

Q. "To call a dimensional quantity 'large' or 'small' is meaningless without specifying a standard for comparison." In view of this, which of the following statements are complete :
(a) atoms are very small objects
(b) a jet plane moves with great speed
(c) the mass of Jupiter is very large
(d) the air inside this room contains a large number of molecules
(e) a proton is much more massive than an electron
(f) the speed of sound is much smaller than the speed of light.

Q. A physical quantity P is related to four observables a, b, c and d as follows :
P $a^3{b}^2$ / $\sqrt{c}$ d
The percentage errors of measurement in a, b, c and d are 1%, 3%, 4% and 2%, respectively. What is the percentage error in the quantity P ? If the value of P calculated using the above relation turns out to be 3.763, to what value should you round off the result ?

Q. A famous relation in physics relates 'moving mass' m to the 'rest mass' $m_0$ of a particle in terms of its speed v and the speed of light, c. (This relation first arose asa 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.

Q. State the number of significant figures in the following:

Q. Write the number of significant digits in 0.6464 :

1. 4
2. 3
3. None of the above
4. 5

Q. 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?

1. $0.035mm$
2. $0.007mm$
   
3. $3.5mm$
   
4. None of the above