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ore, , +m, , , , UNITS MEASUREMENTS AND ERROR ANALYSIS., , Numericals, , e, , atoms are in the earth? Ans. 9.0 x 10, 6. The density of water of 4°C is 1.00 g cm. Find its value in SI. Ans. 1.00 x 10° kg m™ 7. The acceleration of a body is 10 ms 2. Express it in kmh ~. Ans. 1.296 x 10° kmh”., 8. The value of universal gravitation constant G = 6.67 10°! 'Nm?* kg™. Find its value in g™ cm ie, Ans. 6.67 10°, 9. The value of Stefan's constant o = 5.67 x 10° ergs? cm K~* . Vind its value in SI., Given 1 J = 10° erg By mt, TZ. Ans. 5.67x10°Js m“K™., , 10., , 11., , 12., , 13., , 14., , 15., , 16., , WwW,, , 1., , 19,, , . Calculate the number of metric tons in a teragram., . The mass of a proton is 1.67 « 10°” kg. How many protons would make 1 g? Express in a, , . Find the number of hydrogen atoms required to obtain 1.0 kg of hydrogen. Take the mass of gne, , . The earth has a mass of 5.98 » 1077 kg. The average mass of the atoms of earth is 40 u. How many, , The mean wavelength of yellow light from a sodium lamp is 5893 A. Write it in m and nm., Ans. 5.893 x 10°” m, 589.3 nm ., , Ans. 10°., r of, magnitude also. ‘Ans. 5.99 x 107°, 10, , hydrogen atom to be 1.0 u. Given : 1.0 u = 1.66 x 10°77 kg. Ans. 6.0 « 10°., , , , Express the speed of light (= 3.0 « 10° ms“) in terms of AU min '. (Take 1 AU = 1.50 x 10° km), Ans. 0.12 AU min”., If the speed of light is the new unit of speed and year the new unit of time, then what will be the, new unit of length? What is its name? Given : ¢ = 3 x 10° ms! and 1 year = 3.154 x 10’ s., Ans. 9.46 x 10'° m. 1 light year ., , In successive experimental measurements, the refractive index of glass turned out to be 1.54, 1.45,, 1.53, 1.56, 1.44 and 1.54. Compute (1) mean refractive index, (ii) mean absolute error, (iii) fractional, error and (iv) percentage error, (\) Express the refractive index with the error limits., , Ans. (i) 1-51, (ii) 0.04, (iii) 0.03, (iv) 3%, (v) 1.51 + 0.04., The measured lengths of two rods are recorded as (35.2 + 0.1) em and (16.8 + 0.2) cm. Write the, sum of the lengths of the two rods with error limits Ans. (52.0 + 3) cm., The initial and final temperatures of a liquid placed on a heater are recorded as (30.6 + 0.2)°C and, (68.3 + 0.1)°C respectively, Calculate the rise in temperature with error limits. Ans. (37.7 + 0.3)°C., The radius of a sphere is expressed as (53 + 0.1) cm. Find the percentage error in the volume of the, sphere. Ans. 5.7 %,, The measured values of mass, length, breadth and thickness of a rectangular block are 39.3 g,, 5.12 cm, 2.56 cm and 0.37 cm respectively. Find the maximum permissible percentage error in the, determination of the density of the material of the block. Ans. 3.54%., , 2, Ifa physical quantity is p = ab and the percentage errors in the measurernents of a, b and c are, , 196, 296 and 3% respectively, find the maximum percentage error in the measurement of physical, (UPB 2015, 14) Ans. 10%.|, The least count of a screw gauge is 0.001 cm. The diameter of a wire measured by it is 0.225 cm,, , Find out the percentage error in this measurement. Ans. 0.4%, if there is an error of 1.5% in the measurement of the radius of a circle, then what will be the, , quantity P., , , , e um percentage error in the measurement of its area? (UPB 2009) Ans. 3.0%,, Find the maximum probable error in measuring the volume of a box of length 24.0 cm, a, 18:6 cm and height 6.0 cm. =

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21., , 22., , 23., , 24., , 25., , 26,, , 27,, , 28., 29., 30., 31., 32,, , 33,, 34,, , 35., , 36., , 37., , i if its le creased by 4%,, in tim i simple pendulum if its length is increasec, Find the percentage of change in e-period of a simple p le., be of the metal are measured. If the, uri i tal, the mass and length of a cul e ast, ees Se stir and length be 3% and 2%, then what will be the maximum error, errors in the measu!, , Ans. 9%,, in density? : is 1 hysical quantities, la S$ = by measuring the physical q, A student determines the value of S from the formula 3, , dc are 1%, 2% and 3% respectively, then what, in the measurements of a, b ani, a, b and c, If the errors in, , Ans, 14%,, , i i ssible error in the value of S? ; ', , Coane erie weighing 4.31 g in a box weighing 1.5 kg. Find the total pina ae, 2 S. 1.5 kg., , iate number of significant figures. :, fee of different line segments of a straight line are 8.26 cm, a . = 6.296 cm. laa a, ay a @ line., the law of addition of significant figures, write the total length o! Posies, , Add the following with due consideration of significant Figures « =, Gi) 3.8x 10% + 42x 1076 Gi) 3.8 x 10°” + 4.2 x 10, Gii) 4.22 x 10° + 3.11 x 107 + 6.003 x 10® (iv) 1.294 cm + 35.1 cm, (v) 348.2 km + 105 km + 143.8 km (vi) 1.5 kg + 264 g + 52 mg., Ans. (i) 4.2 x 10°, (ii) 4.6 x 107, (iii) 3.75 x 10”, (iv) 36.4 em » (v) 597 km, (vi) 1.8 kg., Subtract the following with due consideration of significant figures :, @ 5.0.x 10°4~ 2.5 x 197, Gi) 18.4 cm - 18.132 cm,, Gil) 104.4 g- 2.34 g. (iv) 4.0 x10? kg - 41.72 kg., (v) 172.4 kg - 98.767 g,, Ans. (i) 5.0 x 1074, , » Gi) 0.3 em, (iii) 102.1 g, (iv) 3.6 x 102, Write the value of the product 185 x 1,52, , in significant figures., , kg, (v) 172.3 kg., , Ans. 281., , The side of a square is 1.6 m. Write its area in appropriate significant figures, Ans. 2.6 m’., , The length of a path-strip is 10.53 m and its width is 0.97 m, Compute its area in appropriate, significant figures, Ans. 10 m*, The length, breadth and height of a block are 12.1 cm, 6.3 em and 8.4 mm. Find its volume in, appropriate significant figures, Ans. 64 cm?, Find the volume, in significant figures, of a block of length 20 m, width 25 cm and thicknéss, 13.53 cm, Ans. 0.68 m?, A circle has a diameter of 5.2 em. Write its circumference in significant figures Ans. 16 cm., a ek of a sphere is 4.24 cm. Compute its surface area up to appropriate Significant figures, ees; . 56.5 cm”,, A cylinder has a length of 1.0 x 107! m and diameter of 2.40 x 19-3 m. Find the cea oe area, , and volume of the cylinder with due consideration of significant figures,, , Ans. 4.52 x 1076 m2, 4.5 x 1077 m?, , 4 - of gute area of 3.41 m? and width Of 1.034 m, Find its length in correct, , The volume of a 91.3 g ball is 25 cm®. Find its density in co; aoe

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UNITS, MEASUREMENTS AND ERROR ANALYSIS, 38., , 39., , 40., , 41., 42., , 43., , 44., , 45., , 51, , A body moves 1250 m in 11 s. Find its average speed in correct number of significant figures., Ans. 1.1 x 10? ms"., In a simple pendulum experiment, the measured length of the pendulum is 90.6 x 10-7 m and the, period of oscillation is 1.91 s. Find the value of acceleration due to gravity up to correct significant, figures. Ans. 9.81 ms., The measured mass and diameter of a uniform brass ball are 29.150 x 1073 kg and 1.92 x 10°? m, respectively. Express the density of brass in appropriate significant figures. Ans. 7.87 x 10° kg m?., Express the number of seconds in a day and in a year in orders of magnitude. Ans. 10°, 107., The number of protons and neutrons in the universe is of the order of 10°” and that in the sun is, of the order of 10°”. If we assume that all stars are of the same mass as the mass of sun, then what, would be the order of the number of stars in the universe? : Ans. 10°,, If an atom (size = 10°'° m) were enlarged to the size of earth ( = 10” m), how large would its, nucleus (= 107! m) be? Ans. 107 m., If the universe ( = 107° m) were to shrink to the size of earth (= 10” m), how large would the earth, be? Ans. 10°?? m., The heart beats once in 0.8 s. Find the number of times the heart beats in the life of 60 years of a, man. Ans. 2.37 x 10°.