Unit dimensions and Measurement (Practice Problem) .pdf (p.1-5)Unit,Dimensions and Measurement-Answersheet.pdf (p.6)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 [MP PET 2003] (a) Ohm (b) Volt (c) Mho (d) Newton 4. The dimension of LR are [MP PET 2003] (a) 2T (b) T (c) 1T (d) 2T 5. Dimensions of potential energy are [MP PET 2003] (a) 1MLT (b) 22 TML (c) 21 TML (d) 11 TML 6. The dimensions of electric potential are [UPSEAT 2003] (a) ][122 QTML (b) ][12 QMLT (c) QTML12  (d) QTML22  7. The physical quantities not having same dimensions are [AIEEE 2003] (a) Speed and 2/100)( (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 [MP PET 2002] (a) 122[TML] (b) ][22 TML (c) ][120 TML (d) ][112 TML 9. Which of the following quantities is dimensionless [MP PET 2002] (a) Gravitational constant (b) Planck's constant (c) Power of a convex lens (d) None of these 10. Which of the two have same dimensions [AIEEE 2002]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 [AIEEE 2002] (a) Force per unit volume (b) Energy per unit volume (c) Force (d) Energy 12. Identify the pair whose dimensions are equal [AIEEE 2002] (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: ,tan CzBAyx  where BA, and C are constants. Which of the following do not have the same dimensions [AMU (Eng.) 2001] (a) x and B (b) C and 1z (c) y and AB / (d) x and A 14. 213 QTML is dimension of [RPET 2000] (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 16. Let ][0 denotes the dimensional formula of the permittivity of the vacuum and ][0that of the permeability of the vacuum. If M = mass, L= length, T= time and I= electric current, then [IIT-JEE 1998] (a) ITLM2310][ (b) 24310][ ITLM (c) 220][ IMLT (d) ITML120][ 17. The dimension of quantity )/( RCVL is [Roorkee 1994] (a) [A] (b) 2][A (c) ][1A (d) None of these 18. The quantity ;0tLVX here 0 is the permittivity of free space, L 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 0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) 2421ATLM (b) 242 ATML (c) 24AMLT (d) 2421 ATLM 21. The dimensional formula for impulse is [EAMCET 1981; CBSE PMT 1991; CPMT 1978; AFMC 1998; BCECE 2003] (a) 2MLT (b) 1MLT (c) 12 TML (d) 12 LTM 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;82 Units, Dimensions and Measurement Pb. PMT 2002; UPSEAT 1999; BCECE 2003] (a) 222 TLM (b) 231 TLM (c) 21 TML (d) 22 TML 23. How many wavelength of 86Kr 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] (a) 1/RC and R/L (b) RC/1 and LR / (c) LC/1 (d) LC / 26. In the relation kzeP, P is pressure, z is distance , k is Boltzmann constant and  is temperature. The dimensional formula of  will be [IIT-JEE (Screening) 2004] (a) ][020TLM (b) ][121TLM (c) ][001TLM (d) ][120TLM 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 g metre (b) The new unit of length is 1 metre (c) The new unit of length is 2gmetre (d) The new unit of time is g1 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 4ATQ where A area,T temperature and  is a universal constant. In the 'energy- length- time temperature' (E-L-T-K) system the dimension of  is (a) 2222 KLTE (b) 1221 KLTE (c) 431 KLET (d) 421 KLET 29. The resistive force acting on a body moving with a velocity V through a fluid at rest is given by AVCFD2 where, DC = coefficient of drag, A = area of cross-section perpendicular to the direction of motion. The dimensions of DC 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 mFlPn2 where p is the number of segments of the vibrating string and m is a constant of the string. What are the