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2., , 1. A physical quantity of the dimensions of, length that can be formed out of c, G and, , is [c is velocity of light, G is universal, , , , 4m,, , constant of gravitation and e is charge], INEET 2017}, , 1 2 2 2 We, wsfez]’ efezt], 1/2 ie 16_¢, , |G 4ne, a, , If energy (E), velocity (v) and time (7) are, chosen as the fundamental quantities, the, dimensional formula of surface tension, will be {CBSE AIPMT 2015], , (a) (Ev*T"), (6) Ev 'T*], () Ev2T >), (a) Eev'T, , 3. If dimensions of critical velocity v, of a, , liquid flowing through a tube are expressed, as [1]‘p’r*], where 7, p and rare the, coefficient of viscosity of liquid, density of, liquid and radius of the tube respectively,, then the values of x, y and z are given by, (@t-1-1 [CBSE AIPMT 2015], (b)-14,.-11, , (e)-4-1-1, , (d) 1,.4,1, , 4, If force (F), velocity (v) and time (T) are, , taken as fundamental units, then the, dimensions of mass are [CBSE AIPMT 2014], (a) [FvT~] (&) (FvT™] (0) Fv'T“") (9) IFT}, , 5. In an experiment, four quantities a,b,c and, , d are measured with percentage error 1%,, , 2%, 3% and 4% respectively. Quantity P is, , calculated P = on Error in P is 2013], (a) 14% (b) 10%, (c) 7% (<) 4%, f . 12, 6. The dimensions of (1 £0) ‘i COSE ‘AIPMT 2012], cay (U!T-¥7] ee, (LT) oqeer’’y, , 7. The dimensions of ; egE*, where €p is, permittivity of free space and E is electric, , field, are [CBSE AIPMT 2010}, (a) (ML2T~?] (o) (MET), (e)(MET~)] (d) {MLT~}, , 8. If the dimensions of a physical quantity are, , given by (M°L?T*], then the physical, quantity will be, (a) pressure ifa=1,b=-1c =-2, (b) velocity ifa=1.b=Qc=-1, , (c) acceleration if a =1,b=1,c =-2, (d) force ifa=0,b=-1c =-2, , [CBSE AIPMT 2009]

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we of the following five physical, , po dimensions?, rameters have the same, 0 Energy density [CBSE AIPMT 2008], (ii) Refractive index, (ili) Dielectric constant, (iv) Young's modulus, (v) Magnetic field natem, i i ii, oard on (d) (i) and (v), , (c) @ and (wv), 10, If the error in the measurement of radius of, a sphere is 2%, then the error in the, determination of volume of the sphere, will be {CBSE AIPMT 2008}, (4% = D)6%®-=— (BR =— (I) 2%, 11. Dimensions of resistance in an electrical, circuit, in terms of dimension of mass M, of, length L, of time T and of current J, would, , be {CBSE AIPMT 2007}, (a) (MET T'] (b) [MLET*), (c) (MUT¥"") (0) (MET?), , 42. The velocity v of a particle at time ¢ is, given by v= at + ——, where a,b andc are, t+e, , constants. The dimensions of a,b and c are, respectively {CBSE AIPMT 2006], , (a) (LT~], (Land [T] —(b) (L}, [T] and [L7?), (6) (LT), [LT] and [L] (4) {L), (LT) and (1?), , 13. The ratio of the dimensions of Planck's, constant and that of the moment of inertia, , is the dimension of [CBSE AIPMT 2005}, {a) frequency (b) velocity, (c) angular momenturn {d) time, , 14, The dimensions of universal §ravitational, constant are (CBSE AIPMT 2004, 1992], (a) [AST] (b) IMT], (0) (57?) rey, , 15. The unit of permittivity of free space, £, is, , (a) coulomb/newton-metre (CBSE AlpMT, (6) newton-metre® ‘coulomb? ae, , (c) coulomb? /newton - metre?, (d) coulomb? /(newton -metrey?, , 16. The value of Planck's constant in SI unit is, , (a) 663 x 10" J-s IcBse, (0) 663 x 10 kg-m/s vAIPMT 2002), , (c) 663 x 10° kg-m?, (d) 663 x 10 J-s, , 17. Planck's constant has the dimension, of, (a) linear momentum (CBSE Alrygy 260, (b) angular momentum I, {c) energy, (d) power, , 18. A pair of physical quantities having sam,, dimensional formulais — {Case Aypyyy Stee, (a) force and torque !, (b) work and energy, (c) force and impulse, (d) linear momentum and angular momentum, , 19. The dimensional formula for magnotic, flux is ICBSE AIPMT 1999), (a) (MTA) (b) [MT 242), () (ML 72a] (2) [ML2T-! ‘A2], , 20. The force F on a sphere of radius r moving, in a medium with velocity v is given by, F =6n nrv. The dimensions of nare, (CBSE AIPMT 1997], , (a) [MLS] (b)[MLT?} (oy (MT) (a) (MET, , 21. Which of the following will have the, dimensions of time ? [CBSE AIPMT 1996}, , & L Cc, Le = i =, {a) (Db) (c) (d), , 22. The density of a cube is measured by, measuring its mass and length of its sides., If the maximum error in the measurement, of mass and length are 4% and 3%, respectively, the maximum error in the, , measurement of density will be, (CBSE AIPMT 1996), (a) 7% {c) 12% (Gd) 13%, 0, , 23. An equation is given as G + 4) =b v, , (b) 9%, , whore p = pressure, V = volume and, = absolute temperature. If aand b are, constants, then dimensions of a will be, , [CBSE AIPMT 1996], (a) (MUST?) (o) [MET], () [MLST-") (d) (ML°T], , 24, The percentage errors in the measurement, of mass and speed are 2% and 3%, respeclively. The error in kinelic energy, obtained by measuring mass and speed,, willbe ~ [CBSE AIPMT 1995], , (a) 12% (b) 10% = (c) 8% (d) 2%

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25. Which of the follo, , 26. In a vernier callipers N, , 27., , constant 7 ng is a dimensional, , ICBSE AIPMT 1995}, a ence index {b) Poisson's ratio, lelative density {) Gravitational constant, , divisions of verni, scale coincide with N — 1 divisions of oats, , scale (in which length of one division Is, ee The least count of the instrument, should be (CBSE AIPMT 1994}, (aN (cy) u, Ne ow «CU wey, Ina particular system, the unit of length,, mass and time are chosen to be 10cm, 10g, and 0.1 s respectively. The unit of force in, , (o)N-1, , _ this system will be equivalent to, , 28., , 50., , 31., , (CBSE AIPMT 1994], , (b) 1N (c) 10N (cd) 100 N, Turpentine oil is flowing through a tube of, length / and radius r, The pressure, difference between the two ends of the, tube is p. The viscosity of oil is given by, , = Plt -*), , a 4vl, where, v is the velocity of oil at distance x, from the axis of the tube. The dimensions, of nare {CBSE AIPMT 1993}, , (a) [MPL°T®} (b) [MLT-"] (c) [MU?T-*] (6) (ML'T""], , (a)0.1N, , The time dependence of physical quantity, pis given by p = py exp (- at”), where a is, , a constant and ¢ is the time. The constant a, [CBSE AIPMT-1992}, , (a) is dimensionless (b) has dimensions [T*], (c) has dimensions [T°] (d) has dimensions of p, , If p represents radiation pressure, ¢, represents speed of light and S represents, radiation energy striking unit area per sec., The non-zero integers x, y, z such that, p*S"c? is dimensionless are, , [CBSE AIPMT 1992], (o)x=-1y=1z=1, , (a)x=ty=14z=1, (a) x=1y=12=-1, , (c)x=tLy=-12=1, The dimensional formula for permeability, of free space, pp is [CBSE AIPMT 1991], (a) [MLT®A~} (b) (ML“T?A~*], , (c) [ML'T*A*] (d) [MLT?A~], , 32. A certain body weighs 22.42 g and has a, measured volume of 4.7 cc. The possible, error in the measurement of mass and, volume are 0.01 g and 0.1 cc. Then,, maximum error in the density will be, (CBSE AIPMT 1991], , (b) 2%, , (d} 0.02%, , {a) 22%, (c) 0.2%, , 33. The frequency of vibration f of a mass m, , suspended from a spring of spring constant, k is given by a relation of the type, f =Cm*k", where C is a dimensionless, , constant, ‘he values of x and y are, , [CBSE AIPMT 1990], oh oie mm Yet, xa 50=5 (0) x e* 2, 1 1, -—,ya-— (d) x=--,y=—, (c) x oe 2 (d) x > y es, , 34. According to Newton, the viscous force, acting between liquid layers of area A and, , Av + al du, velocity gradient a is given byF =— 1A a’, where 1)is constant called [CBSE AIPMT 1990], fa} [ML-PT] (b) [M°LT?] (c) [MLET* (a) [ML'T), , 35. The dimensional formula of pressure is, [CBSE AIPMT 1990], , (a) (MLT?] (b) [ME"T?] (@) (MTT?) (d) [MLT*], , 36. The dimensional formula of torque is, , [CBSE AIPMT 1989], (a) (MUT*] (b) (MLT*}, (c) [MET] (d) (ML? T*], , 37. If x= at + bt®, where x is the distance, travelled by the body in kilometer while t, is the time in second, then the unit ofb is, (CBSE AIPMT 1989], , {a)kmis (by) kms (c)kmys* (cd) kms”, 38. Dimensional formula of self-inductance is, [CBSE AIPMT 1989], (a) (MLT@A-?] (o) (META? ], , (c) [MPT*A~y (0) [MTP], , 39. Of the following quantities, which one has, dimensions different from the remaining, three? ; [CBSE AIPMT 1989), , (a) Energy per unit volume, (6) Force per unit area it volume, (C) Product of voltage and charge per unt VOUS,, , (d) Angular momentum

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40., , 41., , 42,, , 43., , , R, , A beam of eloctrons is moving with, constant velocity in a region having, simultaneous perpendicular electric and, magnetic fields of strength 20 Vm™! and, 0.5 T, respectively at right angles to the, direction of motion of the electrons. Then,, the velocity of electrons must be, , (CBSE AIPMT 1996), , (@8ms (b)20m/s (6) 40m/s (a) % ms, , The magnetic field dB due to a small, element at a distance rand carrying, current j is [CBSE AIPMT 1996}, (a) dB = Ho | (=), 4n r, b) dB = Ho j2 (S), tt an. ?, , (c)dB = Ho j2 (*), 4a f, , B= Ho ; ae"), a 4n (5, , A 10 eV electron is circulating in a plane at, right angle to a uniform field of magnetic, induction 10-7 Wb/m* (= 1.0 gauss). The, orbital radius of the electron is, , [CBSE AIPMT 1996], (a) 12cm = (6) 16cm (c) 14cm (d) 180m, , At what distance from a'long straight wire, carrying a current of 12 A will the magnetic, field be equal to 3 x 10-3 Wb/m? ?, , ICBSE AIPMT 1995}, (a) 8x10? m (b) 12 x 107 m, (c) 18x 10 m (d) 24x 10°? m, , A straight wire of diameter 0.5 mm, , carrying a current of 1 A is replaced by, another wire of 1 mm diameter carrying, same current. The strength of magnetic, field far away is ICBSE AIPMT 1995], (a) twice the earlier value, , (b) same as the earlier value, , (c) one-half of the earlier value, , (d) one-quarter of the earlier value, , , An electron enters a region where magnetic, , field (B) and electric field (£) are mutually, , perpendicular, then {CBSE AIPMT 1994], a) it will always move in the direction of B, , (b) it will always move in the direction of E