80 Units Dimensions and Measurement Problems based on units and dimensions 1 Number of base SI units is MP PET 2003 a 4 b 7 c 3 d 5 2 The unit of Planck s constant is RPMT 1999 MP PET 2003 a Joule b Joule s c Joule m d Joule s 3 The unit of reactance is 4 The dimension of are a Ohm b Volt c Mho d Newton a b T c d 5 Dimensions of potential energy are a b 6 The dimensions of electric potential are a b 7 The physical quantities not having same dimensions are c c d d a Speed and b Torque and work c Momentum and Planck s constant d Stress and Young s modulus 8 The dimensional formula for Boltzmann s constant is a b c d 9 Which of the following quantities is dimensionless 10 Which of the two have same dimensions a Gravitational constant b Planck s constant c Power of a convex lens d None of these MP PET 2003 MP PET 2003 MP PET 2003 UPSEAT 2003 AIEEE 2003 MP PET 2002 MP PET 2002 AIEEE 2002 LR2T1 T2 T1 MLT22 TML21 TML11 TML 122 QTML 12 QMLTQTML12 QTML22 2 100 122 TML 22 TML 120 TML 112 TML Units Dimensions and Measurement 81 a Force and strain b Force and stress c Angular velocity and frequency d Energy and strain 11 The dimensions of pressure is equal to 12 Identify the pair whose dimensions are equal a Force per unit volume b Energy per unit volume c Force d Energy a Torque and work b Stress and energy c Force and stress d Force and work 13 A physical quantity x depends on quantities y and z as follows where and C are constants Which of the following do not have the same dimensions 14 is dimension of a x and B b C and c y and d x and A a Resistivity b Conductivity c Resistance d None of these 15 Two quantities A and B have different dimensions Which mathematical operation given below is physically meaningful CPMT 1997 a A B b A B c A B d None of these AIEEE 2002 AIEEE 2002 AMU Eng 2001 RPET 2000 16 Let denotes the dimensional formula of the permittivity of the vacuum and that of the permeability of the vacuum If M mass L length T time and I electric current then IIT JEE 1998 a b d 17 The dimension of quantity is Roorkee 1994 a A b c d None of these 18 The quantity here is the permittivity of free space is length V is potential difference and t is time The dimensions of X are same as that of IIT JEE Screening 2001 a Resistance b Charge c Voltage d Current 19 The unit of permittivity of free space is MP PET 1993 MP PMT 2003 a Coulomb Newton metre b Newton metre2 Coulomb2 c Coulomb2 Newton metre 2 d Coulomb2 Newton metre2 20 Dimensional formula of capacitance is CPMT 1978 MP PMT 1979 IIT JEE 1983 a b c d 21 The dimensional formula for impulse is EAMCET 1981 CBSE PMT 1991 CPMT 1978 AFMC 1998 BCECE 2003 a b c d 22 The dimensions of universal gravitational constant are MP PMT 1984 87 97 2000 CBSE PMT 1988 92 2004 MP PET 1984 96 99 MNR 1992 DPMT 1984 CPMT 1978 84 89 90 92 96 AFMC 1999 NCERT 1975 DPET 1993 AIIMS 2002 RPET 2001 c tanCzBAyx BA 1 zAB 213 QTML 0 0 ITLM2310 24310 ITLM 220 IMLT ITML120 RCVL2 A 1 A 0tLVX 0 L0 2421ATLM 242 ATML24AMLT 2421 ATLM2 MLT1 MLT12 TML12 LTM 82 Units Dimensions and Measurement c a b c 23 How many wavelength of are there in one metre MNR 1985 UPSEAT 2000 a 1553164 13 b 1650763 73 c 652189 63 d 2348123 73 24 Light year is a unit of MP PMT 1989 AFMC 1991 CPMT 1991 a Time b mass c Distance d Energy 25 L C and R represent physical quantities inductance capacitance and resistance respectively The combination which has the dimensions of frequency is IIT JEE 1984 Pb PMT 2002 UPSEAT 1999 BCECE 2003 d a 1 RC and R L b and c d 26 In the relation P is pressure z is distance k is Boltzmann constant and is temperature The dimensional formula of will be a b IIT JEE Screening 2004 d 27 If the acceleration due to gravity be taken as the unit of acceleration and the velocity generated in a falling body in one second as the unit of velocity then a The new unit of length is metre b The new unit of length is 1 metre c The new unit of length is metre d The new unit of time is second 28 The famous Stefan s law of radiation states that the rate of emission of thermal radiation per unit by a black body is proportional to area and fourth power of its absolute temperature that is where area temperature and is a universal constant In the energy length time temperature E L T K system the dimension of is a b c d 29 The resistive force acting on a body moving with a velocity V through a fluid at rest is given by where coefficient of drag A area of cross section perpendicular to the direction of motion The dimensions of are a ML3T 2 b M 1L 1T2 c M 1 L 1 T 2 d M0L0T0 30 The dimensions of angular momentum magnetic moment are a M3 LT 2A2 b MA 1 T 1 c ML2A 2 T d M2 L 3AT2 31 The frequency n of vibrations of uniform string of length l and stretched with a force F is given by where p is the number of segments of the vibrating string and m is a constant of the string What are the dimensions of m a ML 1 T 1 b ML 3 T0 c ML 2 T0 d ML 1 T0 32 Choose the wrong statement s 222 TLM231 TLM21 TML22 TML86KrRC 1LR LC 1LC kzeP 020TLM 121TLM 001TLM 120TLMg2gg14ATQ A T 2222 KLTE1221 KLTE431 KLET421 KLET AVCFD2 DCDCmFlPn2 a A dimensionally correct equation may be correct b A dimensionally correct equation may be incorrect c A dimensionally incorrect equation may be incorrect d A dimensionally incorrect equation may be incorrect 33 A certain body of mass M moves under the action of a conservative force with potential energy V given by where x Units Dimensions and Measurement 83 is the displacement and a is the amplitude The units of K are a Watt b Joule c Joule metre d None of these 34 The Richardson equation is given by The dimensional formula for AB2 is same as that for a IT2 b kT c IK2 d IK2 T 35 If the units of force energy and velocity are 10 N 100 J and 5 ms 1 the units of length mass and time will be a 10m 5kg 1s b 10m 4kg 2s c 10m …