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10., , 11., , 12, , 13., , 14., , 15., , 16., , , , Units and Dimensions, Write down the dimenional formula of impulse, Ans. [MLT -!}., , Impulse = force x time= [MLT-2}x (T] = [MLT -'], What is the dimension of Boltzmann's Constant ?, Ans. [ML? T -2K- 1],, What is the dimension of universal gas constant ?, Ans, [ML?T -?2K- |]., , Write down the dimension of coefficient of viscosity (1)., Ans. [ML-! T-']., , - Write down the dimension of Gravitational Constant., , Ans. [M-! L3T -2]., If L and R represents inductance and resistance respectively, then what, is the dimension of LE ?, , R, Ans, [M °L°T]., , If R and C represents resistance and capacity respectively, then give the, dimension of RC. |, , Ans. [M °L°T]., , . IfL and C represents the inductance and capacity, then write down the, , dimension pf LC., , Ans. [M °L°T?]., , If a current I is flowing through an inductance L, then find the, dimension of LI?., , Ans. [ML?T~?]. ., , If C represents the capacity of a condenser and if V represents the P.d., across its end then find the dimension of CV’., , Ans. (ML?T~7]. ., , Can unit of energy be written as Watt x day ?, , Ans. Yes., , What is the dimension of surface tension ?, , Ans. [MT~-?}., , Write down the dimension of €o., , Ans. (M-'L-3T4A?]., , Write down the dimension of Resistance, R., , Ans. [ML?T-3A-~?]., , Write down the dimension of, , 1, VBo€o, , , , Ans. [M°LT-'A9.

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18., , 19;, , 20., , 21., , 22., , 23:, , Numericals im Physics, , - If force, time and length are taken as fundamental units then calculate ,, , the dimension of surface tension, power and mass., , Ans."FL-!, FLT-", FL- 'T?,, , If force and mass and length are taken as fundamental units, then, calculate the dimension of velocity., , Ans. [eu M_ 3] :, If velocityof light C, the gravitational constant G and plank's constant, , A be chosen as the fundamental units, then find the dimensions of, mass,length and time in the new system., , By ee a 12 solou, Ans..C7h?G 2, © 2 42G?, C12 4? G?, Convert one newtdh into dyne., , Ans. 10° dyne., The dimension of force, F = [MLT-2], Since, N,U, =N,U,, , wowace], = [oan [pose] [=]"- 105 dyne., , If the value of G, the gravitational constant’in.G. G;'S. system is, 6-70 x 10-8, then what is its value in S. I. unit.?, Ans. 6-70 x 10-1, The dimension of G is [M-'L3T-2], we have, NU =N,U, ;, 2, vlsLe] Lil Fey, s =e we =x Lj LT, in, Fine key [eet f=)", “2 1 kg 1 metre, = 6-70 x 10-8 x 10-3 = 6-70 x 10-"!, If the value of pressure is 10° dyne/cm? in C. G. S. system, then, calculate its value in S. I. unit., Ans. 10° N/m?., , Convert.1 H. P. into watt., Ans. 746 watt., , o

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24,, , 25., , 26., , 27., , 28., , 29., , 30., , 31., , Units and Dimensions 5, , The surface tension of liquid in C. G, S, system is 70 dyne/cm then, what will be its value in S. I. unit,, , Ans. 7 x 10-2 N/m., , If the density of wood in C. G. S. system is 0-5 gm/c.c., then what, will be its value in S. I. unit., , Ans. 500 kg/m3,, , If the value of coefficient of viscosity in S. I. unit is 1-2 N sec m-2,, then calculate its value in C. G. S. system., , Ans. 12 dyne sec cm-?., Express 90° in radian, , Ans. > Fadian,, , If the unit of mass, length and time be each doubled, then how the unit, of power will change., , Ans. remain the same., The dimension of power is [ML?T~3], , alleles pelecp|e-aleae, U LMILLILTI “LM ILQUILT, =2%2? K2-221 4 Uz=U;, , In the above question; how the numerical value is affected :, Ans. remain the same., , U, N.=N; U,, , since, U,; = U2 therefore, N2 = N,, , If the unit of length, mass and time be each doubled, then how the unit, of work will change., , Ans. doubled, work = [ML?T-?], , meielcd Gel -Laellc) (eT, Tee ke “LM ILL T;, =2x22x2-2=2 hence, U, = 2U;,, , In the above problem, how its numercial value will change., , Ans. becomes half., Since, N,U, = N,U, , na Pu ty, ‘iis [eI “eh [zc ee, , erg, eee.

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6 Numericals in Physics, , 32. If the unit of mass and length be doubled and that of time is halved,, then how the unit of force, work and power is affected., Ans. Force, Work and Power will increase 16 times, 32 times and 64, times respectively., , 33. Itis observed that the value of acceleration due to gravity ‘g’ at a place, , is 980 cm/sec; obtain its value in a system in which metre is the unit, of length and minute is the unit of time., , Ans. 35280., Since the dimension of g = (LT-2}, U; Lif ty? 10-2 /60 minute]?, N,=N [e] =N e][2] a4 [ =| [? saa, Pet US ‘LEE Ne m minute, , - whe ena., = 980 x 100 * 9 = 35280., , 34. Convert the value of 10 joule on a system which has 1000 grams, 10, cms and 30 seconds as fundamental units., , Ans. 9 x 105 new units., , , , 35. If the displacement of a particle is represented by y=AT+BT? where — —, : = in metre and tf is in second, then calculate the dimension of A and, Ans. [LT-}]; LT=2] |, LH. S.; y = [L], R.H.S.; AT = {L] wy A a =[LT-!], and, BT? = [1] * B=LT-7], , 36. In the above problem what are the units of A and B ?, , Ans. m/sec, m/sec?., , 37. In the above problem, what physical quantities do they represent ?, , Ans. Velocity; Acceleration., , The displacement of a particle is represented by y = Ar+ Br? +Cr,, then what are the dimensions of A, Band C., Ans. [LT-'} (LT-2, (LT3],, L.H. S.; y = [L}, and, R.H. S.; At= [£); * A=L/T=[LT-!], BP=(L); +. B=L/T?=[LT-4], , and Cf = [L]; A CSL? = [ET=3], 39. Calculate the dimension of «, Band ¥ in the equation,, E=0M + $M"! LT-?+yMLT-! where E represents energy., Ans. (L?T-2]; (M2L}, [(LT-"1., , a8.

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40., , 41., , 42., , 43., , 44., , 45., , 46., , 47., , Units and Dimensions i, , The acceleration of a particle is found to depend upon time as follows, , Ct, =At 2, £ +BP +>, , then calculate the dimension of A, B, C and D., Ans, [LT~3]; [LT-4]; (LT-!}; [12]., , , , : . P, In the equation of velocity of sound V = \ = obtain the dimension, , of y, where P and p represent pressure and density respectively., Ans. [M°L° T°}, ., , Obtain the dimension of the constant ‘a’ and ‘b’ involved in the Vander, Waal's equation of state., , (P+ =) (V-b)=nRT, Ans. [ML5T~ 2); [L3)., Check dimensionally wether the equation x = ut + : J? is incorrecn., , Ans. The dimension of each term is same, hence the equation is, “dimensionally correct’; but the equation itself is not correct. The, , coefficient of f? should be 5 and not - i, , A dimensionally correct equation may be wrong but a, dimensionally wrong equation can not be correct., , In the equation given below what are the S. I. units of C, and C), if y, is in metre and t is in second. :, , y =C, sin Cyt., Ans. metre; radian/sec., The speed of a particle as a function of time is represented by V= Ay, cos Agt. What are the dimention and S, I. units of constant A; and A, ?, Ans. [LT~'] and [T~']; their S. I. units are m/sec and radian/sec. :, The acceleration of a particle as a function of time is represented by the, , equation f = C,sinCt. What are the dimension and S.- I. units of, constant C, and C, ?, , Ans, [LT~2]; [T- !J; their S. I. units are m/sec? and radian/sec., , If in the equation y = asin (wt- Kx), y and x stands for distance and t, for time respectively, then find the dimension of a, w, and K., Ans. M°L T°; M°L° T-!; M°L-! TO.