{"id":47188,"date":"2024-02-17T08:01:09","date_gmt":"2024-02-17T02:31:09","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=47188"},"modified":"2024-02-17T16:14:30","modified_gmt":"2024-02-17T10:44:30","slug":"plus-one-physics-chapter-wise-questions-answers-chapter-2","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/plus-one-physics-chapter-wise-questions-answers-chapter-2\/","title":{"rendered":"Plus One Physics Chapter Wise Questions and Answers Chapter 2 Units and Measurement"},"content":{"rendered":"
Question 1. Question 2. (a) (1)only Question 3. Question 4. Question 5. Question 6. Question 7. Question 8. Question 9. Question 10. Question 11. Question 1. Question 2. Question 3. Answer: 2. l ly= 9.46 \u00d7 1015<\/sup> m Question 4.<\/p>\n Answer:<\/p>\n Question 5. Question 6. Question 7. Answer: 2. 3.9 \u00d7 105<\/sup> – 2.5 \u00d7 104<\/sup> Question 8. Question 9.<\/p>\n Answer: 2. The measurements according to least count:<\/p>\n Question 1. Answer: 2. Dimension of H = L Question 2. Question 3. Answer: 2. The method of dimensional analysis has the following drawbacks:<\/p>\n Question 4. Answer: 2. V = at2<\/sup> + bt + c Question 5. Answer: 2. Question 6. Answer: 2. Question 7. Answer: 2. percentage error = \\(\\frac{\\Delta \\mathrm{a}_{\\text {mean }}}{\\mathrm{a}_{\\text {mean }}}\\) \u00d7 100 Question 8. Answer: 2. F = AB + (P+Q)Y Question 9.<\/p>\n Answer: (ii) L.C of optical instrument = 6000A\u00b0 2. Yes. Because L.C proportional to number of division on the headscale. So with the increase in number of divisions, the least count will increase. This leads to increase the accuracy of above screw guage.<\/p>\n Question 1. Answer: 2. Absolute error, 3. Percentage error = \\(\\frac{\\Delta \\mathrm{m}_{\\text {mean }}}{\\mathrm{m}_{\\text {mean }}}\\) \u00d7 100 Question 2. Answer:<\/p>\n The period of the simple pendulum may possibly depend upon:<\/p>\n Let us write the equation for the time period as t = k ma<\/sup> lb<\/sup> gc<\/sup> qd<\/sup> a = 0; b + c = 0; -2c = 1 Question 1. Answer: 2. The absolute error in each measurement. 3. mean absolute error = |\u2206m1<\/sub>| + |\u2206m2<\/sub>|………..+|\u2206m5<\/sub>|<\/span> 4. Relative error = \u03b4m = \\(\\frac{\\Delta \\mathrm{m}_{\\text {mean }}}{\\mathrm{m}_{\\text {mean }}}=\\frac{.014}{2.52}\\) = 0.00555<\/p>\n 5. Percentage error \u03b4m \u00d7 100 = 0.555%.<\/p>\n Question 1. Answer:
\nHow many seconds are there in a light fermi?
\n(a) 10-15<\/sup>
\n(b) 3.0 \u00d7 108<\/sup>
\n(c) 3.33 \u00d7 10-24<\/sup>
\n(d) 3.3 \u00d7 10-7<\/sup>
\nAnswer:
\n(c) 3.33 \u00d7 10-24<\/sup>
\nOne light fermi is time taken by light to travel a distance of 1 fermi ie. 10-15<\/sup>m
\n1 light fermi = \\(\\frac{10^{-15}}{3 \\times 10^{8}}\\) = 3.33 \u00d7 10-24<\/sup>s.<\/p>\n
\nWhich of the following pairs have same dimensional formula for both the quantities?<\/p>\n\n
\n(b) (2) only
\n(c) (1) and (3) only
\n(d) All of three
\nAnswer:
\n(c) (1) and (3) only<\/p>\n
\nGive four dimensionless physical quantities.
\nAnswer:
\nAngle, Poisson\u2019s ratio, strain, specific gravity.<\/p>\n
\nThe dimensions of plank constant are the same as those of______.
\nAnswer:
\nAngular momentum<\/p>\n
\nA physical quantity P = \\(\\frac{\\sqrt{a b c^{2}}}{d^{3}}\\) measuring a, b, c and d separately with the percentage error of 2% , 3%, 2% and 1% respectively. Minimum amount of error is contributed by the measurement of
\n(a) b
\n(b) a
\n(c) d
\n(d) c
\nAnswer:
\n(b) a
\nP = \\(\\frac{\\sqrt{a b c^{2}}}{d^{3}}\\)
\n
\nThe minimum amount of error is contributed by the measurement of a.<\/p>\n
\nThe number of significant figures in 11.118 \u00d7 10-6<\/sup> is
\n(a) 3
\n(b) 6
\n(c) 5
\n(d) 4
\nAnswer:
\nAs per rules, number of significant figures in 11.118 \u00d7 10-6<\/sup> is 5.<\/p>\n
\nWhat is the number of significant figures in 0.06070?
\nAnswer:
\n4.<\/p>\n
\nIf f = x2<\/sup>, What is the relative error in f?
\nAnswer:
\n\\(\\frac{2 \\Delta x}{x}\\).<\/p>\n
\nWhich of the following measurement is more accu\u00acrate?
\n(i) 7000m
\n(ii) 7 \u00d7 102<\/sup>m
\n(iii) 7 \u00d7 103<\/sup>m
\nAnswer:
\n(i) 7000 m<\/p>\n
\nWhich of the following measurements is most, accurate?
\n(a) 5.0 cm
\n(b) 0.005 cm
\n(c) 5.00 cm
\nAnswer:
\n(c) Is most accurate because it has three significant figures. Greater is number of significant figures, more accurate is the measurement.
\n(a) has 2 significant figures
\n(b) has 1 significant figure.<\/p>\n
\nName three physical quantities having same dimension.
\nAnswer:
\nWork, Energy, and Torque.<\/p>\nPlus One Physics Units and Measurement Tw0 Mark Questions and Answers<\/h3>\n
\nUsing dimensional analysis derive the relation F = ma. Where the symbols have the usual meaning.
\nAnswer:
\nForce on a body depends on mass(m), acceleration (a) an
\nF \u03b1 ma<\/sup>ab<\/sup>tc<\/sup>
\nM1<\/sup>L1<\/sup>T-2<\/sup> = Ma<\/sup>(LT-2<\/sup>)b<\/sup>Tc<\/sup>
\nM1<\/sup>L1<\/sup>T-2<\/sup> = Ma<\/sup>Lb<\/sup>T-2a+c<\/sup>
\nEquating the powers, we get a = 1 ,b = 1, -2b + c = -2, c = 0
\nF = m1<\/sup>a1<\/sup>t0<\/sup> = ma.<\/p>\n
\nUse your definition to explain how simple harmonic motion can be represented by the equation y = a sin \u03c9t
\n(a) Show that the above equation is dimensionally correct
\nAnswer:
\nY = a sin \u03c9t
\nsin \u03c9t has no dimensions. Hence we get L = L
\nHence this equation is dimensionaly correct.
\n<\/p>\n
\nFill in the blanks.<\/p>\n\n
\n1. Curved area = 2\u03c0l
\n= 2 \u00d7 3.14 (2 \u00d7 102<\/sup>) \u00d7 20 \u00d7 102<\/sup>
\n= 2.51 \u00d7 10-6<\/sup>m2<\/sup><\/p>\n
\nlm = \\(\\frac{l \\mathrm{ly}}{9.46 \\times 10^{15}}\\) \u2248 10-6<\/sup>ly.<\/p>\n\n
\n1 light year, 1 parsec, 1 astronomical unit<\/li>\n<\/ol>\n\n
\nMagnitude of force F experienced by a certain object moving with speed V is given by F = KV2<\/sup>. Where K is a constant. Find the dimensions of K.
\nAnswer:
\nF = KV2<\/sup>
\n<\/p>\n
\nWhat is the maximum percentage error in the measurement of kinetic energy if percentage errors in mass and speed are 2% and 3% respectively?
\nAnswer:
\nE = \\(\\frac{1}{2}\\)v2<\/sup>
\n
\n% error in KE = % error in mass + 2 \u00d7 % error in speed
\n= 2% + 2 \u00d7 3% = 8%.<\/p>\n
\nSolve the following with regard to significant figures.<\/p>\n\n
\n1. 5.8 + 0.125 = 5.925
\nRounding to first decimal point, we get 5.9<\/p>\n
\n= 3.5 \u00d7 105<\/sup> – 0.25 \u00d7 104<\/sup>
\n= 3.65 \u00d7 105<\/sup>
\nRounding to first decimal place, we get 3.6 \u00d7 105<\/sup>.<\/p>\n
\nWhat is maximum fractional error in
\ni) (a + b)
\nii) a – b
\niii) ab
\niv) \\(\\frac{a}{b}\\)
\nGiven \u2206 a and \u2206 b are absolute errors in measurements a and b.
\nAnswer:
\n<\/p>\n\n
\n
\n1. n\\(\\frac{\\Delta a}{a}\\)<\/p>\n\n
Plus One Physics Units and Measurement Three Mark Questions and Answers<\/h3>\n
\nA stone is thrown upwards from the ground with a velocity \u2018u\u2019.<\/p>\n\n
\n1. H = \\(\\frac{u^{2}}{2 g}\\) ___(1)
\nu = u, v = o, a = -g, h = ?
\nWe can find maximum height using the equation
\nu2<\/sup> = u2<\/sup> + 2as
\n0 = u2<\/sup> + 2 \u00d7 -g \u00d7 H
\n2gh = u2<\/sup>
\nH = \\(\\frac{u^{2}}{2 g}\\)<\/p>\n
\nDimension of u = (LT-1<\/sup>)
\nDimensions of time (t) = T
\nDimension of g = (LT-2<\/sup>)
\nsubstituting these values in eq(1) we get
\nL = \\(\\frac{\\left(L T^{-1}\\right)^{2}}{\\left(L T^{-2}\\right)}\\)
\nL = L.<\/p>\n
\nDerive an empirical relationship for the force experienced on the car in terms of mass of the car m, velocity v, and radius of the track r using dimensional analysis.
\nAnswer:
\nCentripetal force may depends on mass (m),radius(r) and velocity(v)
\nF \u03b1 ma<\/sup>rb<\/sup>vc<\/sup>
\nM1<\/sup>L1<\/sup>T-2<\/sup> = Ma<\/sup>Lb<\/sup>(LT-1<\/sup>)c<\/sup>
\nM1<\/sup>L1<\/sup>T-2<\/sup> = Ma<\/sup>Lb<\/sup>Lc<\/sup>T-c<\/sup>
\nM1<\/sup>L1<\/sup>T-2<\/sup> = Ma<\/sup>Lb+c<\/sup>T-c<\/sup>
\nEquating we get a = 1, b + c = 1, c = 2, b = -1
\nSubstituting these values in eq(1),we get
\nF = \\(\\frac{M V^{2}}{r}\\).<\/p>\n
\nDimensional formula of a physical quantity indicate how many times fundamental quantity is involved in the measurement of the quantity.<\/p>\n\n
\n1. F = \u03b7A\\(\\frac{d V}{d x}\\)
\n<\/p>\n\n
\nof two, or more terms.<\/li>\n
\nPrinciple of homogeneity is based on the fact that two quantities of same nature can be added.<\/p>\n\n
\n1. For the correctness of an equation, the dimensions on either side must be the same. This is known as the principle of homogeneity of dimensions.<\/p>\n
\nM0<\/sup>L1<\/sup>T-1<\/sup> = aT2<\/sup> + bT + c
\nAccording to principle of homogenity, we get
\naT2<\/sup> = M0<\/sup>L1<\/sup>T-1<\/sup>
\na = \\(\\frac{\\mathrm{M}^{0} \\mathrm{L}^{1} \\mathrm{T}^{-1}}{\\mathrm{T}^{2}}\\)
\n= M0<\/sup>L1<\/sup>T-3<\/sup>.<\/p>\n
\nIf x = a + bt + ct2<\/sup> where x is in meter and t in second.<\/p>\n\n
\n1. According to principle of homogeneity, the dimensions of both sides must be same.
\nie. L = a + bT + cT2<\/sup>
\nie : L = bT, b = L\/T<\/p>\n
\n
\n% error in x = 3 \u00d7 %. error in ‘t’ = 3 \u00d7 2% = 6%.<\/p>\n
\nA physical quantity P is related to four observables a, b, c as P = \\(\\frac{a^{3} b^{2}}{\\sqrt{c d}}\\). The % error in the measurement of a, b, c, and d are 1%, 3%, 4%, 2% are respectively.<\/p>\n\n
\n1. The result of every measurement by any measuring instrument contains some uncertainty. This uncertainty is called error.<\/p>\n
\n
\n% error in
\nP = 3 \u00d7 1 + 2 \u00d7 3 + 1\/2 \u00d7 4 + 1\/2 \u00d7 2
\n= 3 + 6 + 2+ 1
\nP = 12%<\/p>\n
\nRahul measured the height of Ramesh in different trials as 1.67m, 1.65m 1.64m, and 1.63m.<\/p>\n\n
\n1. Arithametic mean,
\n
\namean<\/sub> = 1.645m = 1.65
\nabsolute error,
\n\u2206a1<\/sub> = amean<\/sub> – a1<\/sub>
\n\u2206a1<\/sub> = 1.65 – 1.67 = -0.02
\n\u2206a2<\/sub> = 1.65 – 1.65 = 0
\n\u2206a3<\/sub> = 1.65 – 1.64 = 0.01
\n\u2206a4<\/sub> = 1.65 – 1.63 = 0.02
\nMean absolute error
\n
\n= 0.012<\/p>\n
\n= \\(\\frac{0.012}{1.65}\\) \u00d7 100
\n= 0.75%.<\/p>\n
\nIn a particular experiment Ramu used the relation F = AB + (P + Q) Y to calculate force.<\/p>\n\n
\n1. Principle of homogenity<\/p>\n
\nF = AB + PY + QY
\nMLT-2<\/sup> = AB + PY+ QY
\nAccording to principle of homogeneity
\nMLT-2<\/sup> = PY
\nM1<\/sup>L1<\/sup>T-2<\/sup> = P M0<\/sup>L1<\/sup>T-1<\/sup>
\nie. P = \\(\\frac{M^{\\prime} L^{1} T^{-2}}{M^{0} L^{1} T^{-1}}\\) = M1<\/sup>T-3<\/sup><\/p>\n\n
\n
\n1. (i) L.C of vernier caliperse = \\(\\frac{1}{40}\\) = 0.025mm
\n= 0.025 \u00d7 10-3<\/sup>m
\n= 2.5 \u00d7 10-5<\/sup>m.<\/p>\n
\n= 6000 \u00d7 10-10<\/sup>m
\n(Taking \u03bb of visible light = 6000\u00b0A)= 6 \u00d7 10-7<\/sup>m<\/p>\nPlus One Physics Units and Measurement Four Mark Questions and Answers<\/h3>\n
\nIn an experiment with common balance the mass of a body is found to 2.52g, 2.53g, 2,51g, 2.49g and 2.54g in successive measurements. Calculate<\/p>\n\n
\n1. Mean value, Mmean<\/sub>
\n= \\(\\frac{2.52+2.53+2.51+2.49+2.54}{5}\\)
\n= 2.5g<\/p>\n
\nAbsolute error \u2206m1<\/sub> = |2.52 – 2.52| = 0
\n\u2206m2<\/sub> = |2.52 – 2.53| = 0.01
\n\u2206m3<\/sub> = |2.52 – 2.51| = 0.01
\n\u2206m4<\/sub> = |2.52 – 2.49| = 0.03
\n\u2206m5<\/sub> = |2.52 – 2.54| = 0.02
\n\u2234 Mean absolute error
\n\\(\\frac{0+0.01+0.01+0.03+0.02}{5}\\)
\n\u2206mmean<\/sub> = 0.014g<\/p>\n
\n= \\(\\frac{0.014}{2.52}\\) \u00d7 100 = 0.556.<\/p>\n
\nWhile discussing the period of a pendulam, one of the student argued that period depends on the mass of the bob.<\/p>\n\n
\n
\n
\nwhere, k is a constant having no dimensions; a, b, care to be found out.
\nThe dimensions of, t = T1<\/sup>
\nDimensions of. m = M1<\/sup>
\nDimensions of, l = L1<\/sup>
\nDimensions of, g = L1<\/sup>T-2<\/sup>
\nAngle q has no dimensions (since, q = arc\/radius = L\/L)
\nEquating the dimensions of both sides of the equation, we get,
\nT1<\/sup> = Ma<\/sup>Lb<\/sup> (L1<\/sup>T-2<\/sup>)c<\/sup>
\nie. T1<\/sup> = Ma<\/sup>Lb+c<\/sup>+ T-2c<\/sup>.
\nThe dimensions of the terms on both sides must be the same. Equating the powers of M, L and T.<\/p>\n
\n\u2234 c = –<\/sup>\\(\\frac{1}{2}\\), b = –<\/sup> c = \\(\\frac{1}{2}\\)
\nHence, the equation becomes,
\nt = kl1\/2<\/sup>g-1\/2<\/sup>
\nie, t = k\\(\\sqrt{1 \/ g}\\)
\nExperimentally, the value of k is found to be 2p.<\/p>\nPlus One Physics Units and Measurement Five Mark Questions and Answers<\/h3>\n
\nIn an experiment with a common balance the mass of a ring found to be 2.52g, 2.5g, 2,51g, 2.49g and 2.54g in successive measurements. Calculate<\/p>\n\n
\n1. The mean value of the mass of the ring.
\nMmean<\/sub> = \\(\\frac{2.52+2.53+2.51+2.49+2.54}{5}\\) = 2.52g.<\/p>\n
\n\u2206m1<\/sub> = Mmean<\/sub> – m1<\/sub> = 2.52 – 2.52 = 0.00
\n\u2206m2<\/sub> = Mmean<\/sub> – m2<\/sub> = 2.52 – 2.53 = -0.01
\n\u2206m5<\/sub> = Mmean<\/sub> – m5<\/sub> = 2.52 – 2.54 = -0.02<\/p>\n
\n= 0.014<\/p>\nPlus One Physics Units and Measurement NCERT Questions and Answers<\/h3>\n
\nFill in the blanks:<\/p>\n\n
\n1. V = (1 cm)3<\/sup>
\n= (10-2<\/sup>m)3<\/sup>
\n= 10-6<\/sup>m3<\/sup>
\nSo, answer is 10-6<\/sup>.<\/p>\n