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Units, Dimension And Measurement Mcq
Quiz 1
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Q.1
Which of the following represents dimensional co-efficient of viscosity?
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a) M1L2T-2
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b) M1L1T-1
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c) M1L2T-1
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d) M1L-1T-1
Explanation
Answer : (d)
Q.2
Which one of following is not the vector quantity?
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a) torque
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b) displacement
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c) velocity
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d) speed
Explanation
speed is the quantity which requires only magnitude Answer : (d)
Q.3
Dimension of torque are [AFMC 1997]
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a) [ M2 L2 T2 ]
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b) [ M L2 T-2 ]
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c) [ M L2 T-1 ]
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d) [ M L2 T-1 ]
Explanation
Torque = I × α = [ ML2 ]×1/[ T2 ] = [M L2 T-2 ] Answer: (b)
Q.4
If the error in the measurement of the momentum of a particle is (+100%). Then the error in the measurement of kinetic energy is [AFMC 1998]
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a) 400%
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b) 300%
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c) 100%
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d) 200%
Explanation
The error in momentum p is 100% therefore reading is 2p. Hence, new kinetic energy K' = 4p2/2m Error in Kinetic energy = [(K'-K)/K] × 100. On substituting the values we get error = 300% Answer: (b)
Q.5
Dimensions of impulse are
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a) [ M L-2 T-3 ]
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b) [ ML-2 ]
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c) [ M L T-1 ]
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d) [MLT-2]
Explanation
Impulse = Force × time =[M L T-2] × [T] = [ M L T-1 ] Answer: (c)
Q.6
The dimension of gravitational constant G is
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a) [ML-2T-3]
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b) [ML-2]
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c) [ML-2T2]
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d) [M-1L3T-2]
Explanation
F = [G × m1 m2] / r2 G = [F . r2] / m1 m2 G = [MLT-2] × [L2] / [M2] G = [M-1 L3 T-2] Answer: (d)
Q.7
The number of significant figures in 3400 is [AFMC 2000]
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a) 7
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b) 6
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c) 12
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d) 2
Explanation
The number of significant figures in 3400 is 2 Answer: (d)
Q.8
Weber/m2 is equal to
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a) dyne
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b) tesla
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c) watt
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d) henry
Explanation
Weber/m2 is the unit of magnetic field which is equal to tesla. Answer: (b)
Q.9
The dimensions of Planck's constant are
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a) [ML-3T-2]
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b) [ML-2T-1]
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c) [ML2T-3]
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d)[ML2T-1]
Explanation
hv = E h = E/v = [ML2T-2] / [1/T] = [ML2T-1] Answer: (d)
Q.10
Chronometer measures [AFMC 2003]
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a) area
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b) time
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c) length
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d) temperature
Explanation
Chronometer is a very accurate time keeper, used for the determination of longitude on board ship by means of celestial navigation. Answer: (b)
Q.11
Which is not a unit of time? [AFMC 2003]
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a) leap year
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b) year
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c) second
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d) light year
Explanation
Light year is a unit of a distance and not time. It is distance travelled by light in one year. Answer:(d)
Q.12
Which one is a vector quantity? [AFMC 2003]
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a) Time
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b) temperature
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c) flux density
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d) magnetic field intensity
Explanation
Magnetic field intensity is a vector quantity. Any field whether gravitational, magnetic or electric must have direction. Answer: (d)
Q.13
Light year is unit of [AFMC 2005]
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a) time
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b) speed
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c) distance
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d) none of these
Explanation
light year is the distance traveled by light in a period of time of 1 year, so it is unit of distance. Answer: (c)
Q.14
If error in measurement of radius of sphere is 1%, what will be the error in measurement of volume? [AFMC 2005]
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a) 1%
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b) 1/3%
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c) 3%
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d) 10%
Explanation
V = (4/3)π r3 so, if error in r is 1% % error in volume = (3 × 1)% = 3% Answer: (c)
Q.15
Minimum number of unequal vectors which can give zero resultant are [ AFMC 2005]
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a) 2
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b) 3
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c) 4
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d) more than four
Explanation
Minimum number of unequal vectors giving zero resultant will be three. The resultant of first two will be equal and opposite to third vector. Answer: (b)
Q.16
"Pascal second" has the dimensions of [AFMC 2005]
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a) force
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b) energy
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c) pressure
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d) coefficient of viscosity
Explanation
Pascal second = (F/A) × T Pascal second = ([M L T-2] × [T])/ [L2] Pascal second =[M L-1 T-1] It is the dimensional formula of viscosity Answer: (d)
Q.17
magnetic moment has dimensions of [AFMC 2006]
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a) [LA]
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b) [L2A]
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c) [LT-1A]
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d) [L2TL-1A]
Explanation
Magnetic moment of a current carrying coil having area A is given as Answer: (b)
Q.18
What are the dimensions of permeability
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a) [M1 L1 T1 A-2 ]
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b) [M1 L1 T-2 A-2 ]
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c) [M2 L2 T1 A0 ]
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d) [M1 L2 T2 A-2 ]
Explanation
The magnetic field at a point near a long straight conductor is given by Answer: (b)
Q.19
Which of the following are not the units of self inductance? [AFMC 2010]
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a) Weber/Ampere
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b) Ohm-Second
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c) Joule-Ampere
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d) Joule-Ampere-2
Explanation
L = Φ/i. Hence unit of inductance is Weber/amper Also ε= L( di/dt) L = ε(dt/di) hence other units are ohm second and joule/ ampere2 Answer: (c)
Q.20
The dimensional formula for magnetic flux is [AFMC 2010]
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a) [M1 L2 T-1 C-1]
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b) [M1 L2 T-2 C-1]
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c) [M1 L2 T-2 C-1]
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d) [M1 L2 T-2 C-3]
Explanation
Φ= BA [M1 L2 T-1 C-1] Answer: (a)
Q.21
The resistance R of a wire is given by the relation Percentage error in the measurement of ρ, l and r is 1%, 2% and 3% respectively. Then the percentage error in the measurement of R is AFMC 2011]
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a) 6
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b) 9
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c) 8
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d) 10
Explanation
Percentage error= Percentage error=1%+2%+2×3%=9% =9% Answer: (b)
Q.22
A wire has length l = (6 ± 0.06) cm, radius r = (0.5 ± 0.005)cm and mass m = (0.3 ± 0.003) g Maximum percentage error in density...
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a) 4
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b) 2
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c) 1
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d) 6.8
Explanation
density ρ = M/V Volume of cylinder V = πr2l ∴ ρ M/ (πr2l) percentage error = relative error × 100 percentage error = 0.04× 100 percentage error = 4 Answer: (a)
Q.23
The displacement of particle moving along x-axis with respect to time is x = at +bt2 - ctThe dimensions of c are
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a) T-3
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b) LT-1
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c) LT-3
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d) LT-2
Explanation
Each term on RHS must have dimensions of displacement ct3 = x ∴ c = x/t3 dimensions of c = L/T3 dimensions of c = LT-3 Answer: (c)
Q.24
The length and breadth of a metal sheet are 3.124m and 3.002m respectively. The area of this sheet up to four correct significant figure is ... [ AIIMS 2001]
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a) 9.378 m2
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b) 9.37 m2
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c) 9.378248 m2
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d) 9.3782 m2
Explanation
Area of metal sheet = 3.124 × 3.002 Area = 9.378248 Now, the result must have significant figures equal to the least of figure being multiplied. So, Area of metal sheet = 9.378 m2 Answer:(a)
Q.25
If time period of oscillation of a pendulum is measured as 2.5 second using a stop watch with least count 0.5 sec, then the permissible error in the measurement is ..
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a) 10%
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b) 30%
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c) 20%
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d) 25%
Explanation
Here T = 2.5sec ΔT = 0.5 sec Percentage error in time = (ΔT / T )× 100 = (0.5 / 2.5) × 100 = 20% Answer: (c)
Q.26
Using mass (M), length (L) and time (T) and current (A) as fundamental quantities , the dimensions of permeability are .. [ AIIMS 2003]
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a) [ M-1LT-2A]
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b) [ ML-2 T-2A-1]
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c) [MLT-2A-2]
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d) [ MLT-1A-1]
Explanation
Force on charge due to magnetic field is F = B.q.V q = charge = I.t I = current ; t = time V = velocity of charge particle B = magnetic field = µ.n.I µ = permeability, n = number of turns per unit length Thus F = µ.n.I.q.V Answer: (c)
Q.27
The speed of light (c), gravitational constant (G) and Plank's constant(h) are taken as fundamental units in a system. The dimensions of time in this new system should be... [ AIIMS 2008]
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a)G1/2h1/2c-5/2
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b) G-1/2h1/2c1/2
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c) G1/2h1/2c-3/2
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d) G1/2h1/2c1/2
Explanation
let time T ∝ cx.Gy.hz T = cx.Gy.hz Taking dimensions on both side [M0L0T1] = [LT-1]x [ M-1L3 T-2]y [ ML2T-1]z [M0L0T1] = M-y+zLx+3y+2z T-x-2y-z] Equating power of M, L, T on both side, we get -y + z = 0 ..(1) x + 3y + 2z = 0 ..(2) -x - 2y - z = 1..(3) From (1) z= y Adding (2) and (3) y + z = 1 thus z= y = 1/2 ( as z=y) Putting values in(2) we get x + 3/2 + 1 = 0 or x = -5/2 Answer: (a)
Q.28
Which of the following physical quantities do not have same dimensions? .. [ AIIMS 2007]
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a) pressure and stress
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b) tension and surface tension
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c) strain and angle
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d) energy and work
Explanation
tension is force and surface tension is force per unit area hence there dimensions are not same Answer:(b)
Q.29
Which of the following pair of quantities do not have the same dimensions.. [ AFMC 2011]
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a) potential gradient, electric field
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b) Torque, kinetic energy
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c) light year, time period
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d) Impedance, resistance
Explanation
Light year has the dimension of distance and time period time Answer: (c)
Q.30
"Parsec" is the unit of ... [ AIIMS 2005]
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a) time
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b) distance
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c) frequency
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d) angular acceleration
Explanation
Parsec is the unit of length on astronomical scale. It is the distance of an object that will show a parallax of 1" of arc from opposite side of a baseline ( radius) equal to the distance between sun and earth. 1parsec = 3.1×1016 m Answer: (b)
0 h : 0 m : 1 s
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