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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) the mass of Jupiter is very large (b) the air inside this room contains a large
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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) the speed of sound is much smaller than the speed of
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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
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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
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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
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Answer the following : (a)You are given a thread and a meter 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
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The photograph of a house occupies an area of 1.75 `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 `m^2` . What is the linear magnification of the projector-screen
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Two resistors of resistances `R_1 = 100 ±3` ohm and `R_2 = 200 ± 4` ohm are connected (a) in series, (b) in parallel. Find the equivalent resistance of the (i) series combination, (ii) parallel combination. Use for (a) the relation `R = R_1 + R_2`, and for (b) `1/R^'=1/R_1+1/R_2` and `(∆R^')/(R^('2)) = (∆R_1)/R_1^2+(∆R_2)/R_2^2`
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State the number of significant figures in the following : (a) `0.007 m^2` (b) `2.64 × 10^(24) kg` (c) `0.2370 g
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State the number of significant figures in the following : (d) 6.320 J (e) `6.032 N m^(–2)` (f) `0.0006032
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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
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The mass of a box measured by a grocer’s balance is 2.300 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
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A physical quantity P is related to four observables a, b, c and d as follows : `P=(a^3b^2)/(sqrtcd)` 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
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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=m_o/((1-v^2)^(1/2))` Guess where to put the missing
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The unit of length convenient on the atomic scale is known as an angstrom and is denoted by Å: 1 Å = `10^(–10)` m. The size of a hydrogen atom is about 0.5 Å. What is the total atomic volume in `m^3` of a mole of hydrogen atoms
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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 Å). Why is this ratio so large
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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
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The principle of ‘parallax’ in section 2.3.1 is used in the determination of distances of very distant stars. The baseline AB is the line joining the Earth’s two locations six months apart in its orbit around the Sun. That is, the baseline is about the diameter of the Earth’s orbit `≈ 3 xx 10^(11)`m. However, even the nearest stars are so distant that with such a long baseline, they show parallax only of the order of 1” (second) of arc or so. A parsec is a convenient unit of length on the astronomical scale. It is the distance of an
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The nearest star to our solar system is 4.29 light years away. How much is this distance in terms of parsecs? How much parallax would this star (named Alpha Centauri) show when viewed from two locations of the Earth six months apart in its orbit around the Sun
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Just as precise measurements are necessary in science, it is equally important to be able to make rough estimates of quantities using rudimentary ideas and common observations. Think of ways by which you can estimate the following (where an estimate is difficult to obtain, try to get an upper bound on the quantity) : (a) the total mass of rain-bearing clouds over India during the Monsoon (b) the mass of an elephant (c) the wind speed during a storm (d) the number of strands of hair on your head (e) the number of air molecules in your
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