Q 2.13: A physical quantity P is related to four observables a, b, c and d as follows : 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 2.12: The mass of a box measured by a grocer’s balance is 2.30 kg. Two gold pieces of masses 20.15 g and 20.17 g 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?
The difference in the masses of the pieces = 20.17 - 20.15 = 0.02 g (which has only one significant digit !)
Since two is the least number of decimal places, the total mass = 0.02 g.
Q 2.11: 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 2.9: The photograph of a house occupies an area of 1.75 on a 35 slide. The slide is projected on to a screen, and the area of the house on the screen is 1.55 . What is the linear magnification of the projector-screen arrangement.
2.8 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 1.0 mm 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 2.7: 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?
Q 2.6: Which of the following is the most precise device for measuring length :
(a) a vernier callipers with 20 divisions on the sliding scale
(b) a screw gauge of pitch 1 mm and 100 divisions on the circular scale
(c) an optical instrument that can measure length to within a wavelength of light?
Q 2.5: 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?
Q 2.4: Explain this statement clearly: “To call a dimensional quantity ‘large’ or ‘small’ is meaningless without specifying a standard for comparison”. In view of this, reframe the following statements wherever necessary :
(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 2.3: A calorie is a unit of heat (energy in transit) and it equals about 4.2 J where . Suppose we employ a system of units in which the unit of mass equals , the unit of length equals , the unit of time is . Show that a calorie has a magnitude 4.2 in terms of the new units.
Q) 2.1 Fill in the blanks
(a) The volume of a cube of side 1 cm is equal to .....
(b) The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to ...
(c) A vehicle moving with a speed of covers....m in 1 s
(d) The relative density of lead is 11.3. Its density is .... or .... .