NEET AIPMT Physics Chapter Wise Solutions – Units and Measurements

NEET AIPMT Physics Chapter Wise SolutionsChemistryBiology

1. If dimensions of critical velocity v_c of a liquid flowing through a tube are expressed as [η^xρ^yr^z] where η, ρ and r are 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
(a) -1,-1,-1
(b) 1,1,1
(c) 1,-1,-1
(d) -1,-1, 1 (AIPMT 2015)

2. If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be
(a) [EV^-2T^-2]
(b) [E^-2V^-1T^-3]
(c) [EV^-2T^-1]
(d) [EV^-1T^-2] (AIPMT 2015, Cancelled)

3. If force (F), velocity (V) and time (T) are taken as fundamental units, then the dimensions of mass are
(a) [FVT^-1]
(b) [FVT^-2]
(c) [FV^-1T^-1]
(d) [FV^-1T] (AIPMT 2014)

4. 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 as follows

% error in P is
(a) 7%
(b) 4%
(c) 14%
(d) 10% (NEET 2013)

5. The pair of quantities having same dimensions is
(a) Impulse and Surface Tension
(b) Angular momentum and Work
(c) Work and Torque
(d) Young’s modulus and Energy ( Karnataka NEET 2013)

6. The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are
(a) kg ms^-1
(b) kgms^-2
(c) kg s^-1
(d) kg s (Prelims 2012)

7. The dimensions of are ( μ₀ε₀ )^-2 are

8. The density of a material in CGS system of units is 4 g cm^-3. In a system of units in which unit of length is 10 cm and unit of mass is 100 g, the value of density of material will be
(a) 0.04
(b) 0.4
(c) 40
(d) 400 (Mains 2011)

9. The dimension of ε₀E² , where e0 is permittivity of free space and E is electric field is
(a) ML²T^-2
(b) ML^-1T ^-2
(c) ML²T^-1
(d) MLT^-1 (Prelims 2010)

10. A student measures the distance traversed in free fall of a body, initially at rest, in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are e1 and e₂ respectively, the percentage error in the estimation of g is
(a) e₂-e1
(b) e1 + 2e₂
(c) e1+ e₂
(d) e1-2e₂ (Mains 2010)

11. If the dimensions of a physical quantity are given by _M^a_L^b_T^c, then the physical quantity will be
(a) velocity if a = l,b = 0,c =- 1
(b) acceleration if a = 1, h = l,c = -2
(c) force if a = 0, b = – 1, c = – 2
(d) pressure if a = 1, b = – 1, c= -2 (Prelims 2009)

12. 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
(a) 8%
(b) 2%
(c) 4%
(d) 6% (Prelims 2008)

13. Which two of the following five physical parameters have the same dimensions ?
1. energy density
2. refractive index
3. dielectric constant
4. Young’s modulus
5. magnetic field
(a) 1 and 4
(b) 1 and 5
(c) 2 and 4
(d) 3 and 5 (Prelims 2008)

14. Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and of current I, would be
(a) [ML²T^-2]
(b) [ML²T^-1I^-1  ]
(c) [ML²T^-3I^-2]
(d) [ML²T^-3I^-1] (2007)

15. The velocity v of a particle at time t is given by V=at+ where a, b and c are constants. The dimensions of a, b and c are
(a) [L], [LT] and [LT^-2]
(b) [LT^-2], [L] and [T]
(c) [L²], [T] and [LT^-2]
(d) [LT^-2], [LT] and [L]. (2006)

16. The ratio of the dimensions of Planck constant and that of moment of inertia is the dimensions of
(a) time
(b) frequency
(c) angular momentum
(d) velocity. (2005)

17. The dimensions of universal gravitational constant are
(a) [M^-1L³T^-2]
(b) [ML²T^-1]
(c) [M^-2L³T^-2]
(d) [M^-2L²T^-1] (2004,1992)

18. The unit of permittivity of free space, ε₀, is
(a) coulomb/newton-metre
(b) newton-metre²/coulomb²
(c) coulomb²/newton-metre²
(d) coulomb²/(newton-metre)² (2004)

19. The dimensions of Planck constant equals to that of
(a) energy
(b) momentum
(c) angular momentum
(d) power. (2001)

20. Which pair do not have equal dimensions ?
(a) Energy and torque
(b) Force and impulse
(c) Angular momentum and Planck constant
(d) Elastic modulus and pressure. (2000)

21. The dimensional formula of magnetic flux is
(a) [M⁰L^-2T^-2A^-2]
(b) ML⁰T^-2A^-2]
(c) [ML²T^-2A^-1]
(d) [ML²T^-1A3] (1999)

22. An equation is given here(=)where P = Pressure, V = Volume and 0 = Absolute temperature. If a and b are constants, the dimensions of a will be
(a) [ML^-55T^-1]
(b) [ML⁵T¹]
(c) [ML⁵T^-2]
(d) [M^-1L⁵T²]. (1996)

23. 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 lengths are 3% and 2% respectively, the maximum error in the measurement of density would be
(a) 12%
(b) 14%
(c) 7%
(d) 9%. (1996)

24. The dimensions of impulse are equal to that of
(a) pressure
(b) linear momentum
(c) force
(d) angular momentum. (1996)

25. Which of the following dimensions will be the same as that of time?
(a)
(b)
(c) LC
(d) .(1996)

26. Which of the following is a dimensional constant?
(a) Relative density
(b) Gravitational constant
(c) Refractive index
(d) Poisson ratio. (1995)

27. The dimensions of RC is
(a) square of time
(b) square of inverse time
(c) time
(d) inverse time. (1995)

28. Percentage errors in the measurement of mass and speed are 2% and 3% respectively. The error in the estimate of kinetic energy obtained by measuring mass and speed will be
(a) 8%
(b) 2%
(c) 12%
(d) 10%. (1995)

29. Which of the following has the dimensions of pressure?
(a) [MLT^-2]
(b) [ML^-1T^-2]
(c) [ML^-2T^-2]
(d) [M^-1L^-1]. (1994, 90)

30. Turpentine oil is flowing through a tube of length l and radius r. The pressure difference between the two ends of the tube is P. The viscosity of oil is given by  η= where v is the velocity of oil at a distance x from the axis of the tube. The dimensions of η are
(a) [M⁰L⁰T⁰]
(b) [MLT^-1]
(c) [ML²T^-2]
(d) [ML^-1T^-1] (1993)

31. The time dependence of a physical quantity p is given by p = p0 exp (-a/2), where a is a constant and t is the time. The constant a 
(a) is dimensionless
(b) has dimensions [T^-2]
(c) has dimensions [T²]
(d) has dimensions of p (1993)

32. P represents radiation pressure, c represents speed of light and S represents radiation energy striking per unit area per sec. The non zero integers x, y, z such that P^xS^yc^z is dimensionless are
(a) x= l,y= l,z = 1
(b)x = -l,y=l,z=l
(c) x = l,y = -1, z = 1
(d) x = l,y = 1, z = -1 (1992)

33. A certain body weighs 22.42 g and has a measured volume of 4.7cc. The possible error in the measurement of mass and volume are 0.01 g and 0.1 cc. Then maximum error in the densiy will be
(a) 22%
(b) 2%
(c) 0.2%
(d) 0.02%. (1991)

34. The dimensional formula of permeability of free space μo is
(a) [MLT^-2A^-2]
(b) [M⁰L¹T]
(c) [M⁰L²T^-1A²]
(d) none of these. (1991)

35. The frequency of vibration/of a mass m suspended from a spring of spring constant k is given by a relation / = amxky, where a is a dimensionless constant. The values of x and y are
(a) X= , Y=
(b) X= , Y=
(c)X= , Y=
(d) X= ,Y=(1990)

36. According to Newton, the viscous force acting between liquid layers of area A and velocity gradient Δv/ΔZ is given by F =-ηA , where is constant called coefficient of viscosity. The dimensional formula of q is

37. If x = at + bt2, where x is the distance travelled by the body in kilometers while t is the time in seconds, then the units of h is
(a) km/s
(b) kms
(c) km/s2
(d) kms2. (1989)

38. Of the following quantities, which one has dimensions different from the remaining three ?
(a) Energy per unit volume
(b) Force per unit area
(c) Product of voltage and charge per unit volume
(d) Angular momentum. (1989)

39. Dimensional formula of self inductance is

40. The dimensional formula of torque is

41. If C and R denote capacitance and resistance, the dimensional formula of CR is
(a) [M⁰L⁰T¹]
(b) [M⁰L⁰T⁰]
(c) [M⁰L⁰T^-1]
(d) not expressible in terms of MLT. (1988)

42. The dimensional formula of angular momentum is

Explanations