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Consider a simple pendulum, having a bob attached to a string, that oscillates under the action of the force of gravity. Suppose that the period of oscillation of the simple pendulum depends on its length (l), mass of the bob (m) and acceleration due to gravity (g). Derive the expression for its time period using method of
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Fill in the blanks The volume of a cube of side 1 cm is equal to
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Fill in the blanks The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to
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Fill in the blanks A vehicle moving with a speed of 18 km `h^(–1)` covers....m in 1
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Fill in the blanks The relative density of lead is 11.3. Its density is ....g `cm^(–3)` or ....kg
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Fill in the blanks by suitable conversion of units 1 kg `m^2 s^(–2)` = ....g `cm^2
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Fill in the blanks by suitable conversion of units 1 m = .....
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Fill in the blanks by suitable conversion of units 3.0 m `s^(–2)` = .... km
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Fill in the blanks by suitable conversion of units `G = 6.67 × 10^(–11) N m^(2) (kg)^(–2) = .... (cm)^3 s^(–2) g^(–1)`
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A calorie is a unit of heat or energy and it equals about 4.2 J where 1J = 1 kg `m^2 s^(–2)`. Suppose we employ a system of units in which the unit of mass equals α kg, the unit of length equals β m, the unit of time is γ s. Show that a calorie has a magnitude 4.2 `α^(–1) β^(–2) γ^(2)` in terms of the new
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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) atoms are very small objects (b) a jet plane moves with great
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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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