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Quiz 2
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Q.1
Dimensions of coefficient of viscosity is [ AIIMS 2010]
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a) [M T2]
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b) [ ML-3T-4]
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c) [ M L-1 T-2 ]
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d) [ML-1T-1]
Explanation
Coefficient of viscosity η Force F = MLT-2 Area A = l2 Velocity gradient dV/dx = LT-1 / L = T-1 substituting dimensions in equation for η η = [ML-1T-1] Answer: (d)
Q.2
What is the dimensions of impedance? [ AIIMS 2007]
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a) [ ML2T-3I-2 ]
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b) [ M-1L-2T3I2 ]
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c) [ ML3T-3I-2 ]
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d) [ M-1L-3T3I2 ]
Explanation
Impedance is same as resistance but in a.c. circuit Dimension of impedance = dimension of voltage(V) / dimension of current(I) Dimension of Voltage = [ Ml2T-3I-1] Dimensions of current I = [I] Substituting dimensions in equation for impedance we get = [ ML2T-3I-2 ] Answer:(a)
Q.3
What are the units of
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a) C2N-1m-2
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b) Nm2C-2/
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c) Nm2C2
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d) Unit less
Explanation
According to Coulomb's law Answer: (b)
Q.4
What is the dimensional formula for gravitational constant? [ AIIMS 2000]
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a) [ M L2 T-2]
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b) [ M L-1 T-1]
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c) M-1L3T-2
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d) none of these
Explanation
Formula for gravitational force Answer: (c)
Q.5
The dimensional formula of the constant 'a' in Vender Waal's equation.
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a) [ M L4T-1 ]
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b) [ M L2T-2 ]
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c) [ M L5T-3 ]
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d) [ M L5T-2 ]
Explanation
here dimension of a/V2 will be equal to pressure so Answer: (d)
Q.6
In a slide calliper, (m+1) number of vernier divisions is equal to m number of smallest main scale division s. If d is the magnitude of the smallest main scale division, then the magnitude of the vernier constant is ..... unit
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a)
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b)
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c)
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d)
Explanation
(m+1) V.S.D. = m M.S.D. 1 V.S.D = (m/ m+1) M.S.D. Vernier constant = 1 M.S.D - 1 V.S.D = 1 M.S.D. - (m/m+1) M.S.D = (1/m+1) M.S.D = (d/ m+1) units Answer:(a)
Q.7
A quantity x is given by where ε0 is the permittivity of free space, L is the length, ΔV is a potential difference and Δt is a time interval. The dimensional formula for x is the same as that of .. [ BHU 2013]
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a) resistance
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b) charge
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c) voltage
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d) current
Explanation
The capacitance of a parallel plate capacitor is given by C = ε0A/d Thus dimension of ε0L is that of capacitance Thus dimension of given equation = (Dimension of C × Dimension of V ) / Dimension of Time = Dimension of Q / Dimension of time ( As Q = CV ) = Dimension of current Answer: (d)
Q.8
The density of material in CGS system of unit is 4g/cmIn a system of units in which unit of length is 10cm and unit of mass is 100g, the value of density of material will be.. [ CBSE-PMT 2011]
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a) 0.4
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b) 40
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c) 400
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d) 0.04
Explanation
In CGS system. d = 4 g/ cm3 The unit of mass is 100 g and unit of length is 10cm so, Answer: (b)
Q.9
Which two of the following five physical parameters have the same dimensions? A) Energy Density B) Refractive Index C) Dielectric Constant D) Young's Modulus E)Magnetic Field [ CDSE-PMT 2008]
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a) (B) and (D)
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b) (C) and (E)
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c) (A) and (D)
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d) (A) and (E)
Explanation
Energy density = Work / Volume Energy density = [ M L2T-2] / L3 = [M L-1T-2] Young's Modulus : Y = [M L-1T-2] Answer: (c)
Q.10
If the dimensions of a physical quantity are given by Ma Lb Tc, then the physical quantity will be.. [ CBSE-PMT 2009]
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a) Velocity if a =1, b =0, c = -1
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b) Acceleration if a =1, b=1, c=-2
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c) Force if a=0, b=-1, c =-2
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d) Pressure if a =1, b= -1, c=-2
Explanation
Pressure = ML-1T-2 here a = 1, b=-1, c=-2 Answer:(d)
Q.11
The force F on a sphere of radius 'a' moving in a medium with velocity 'v' is given by F = 6πηav. The dimensions of η are ... [ CBSE-PMT 1997]
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a) [ML-3]
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b) [ML-2]
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c) [ML-1]
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d) [ML-1 T -1]
Explanation
now formula for η will be Answer: (d)
Q.12
The velocity 'v' of a particle at time t is given by where a, b, c are constant then dimensions of a,b, c are respectively [ CBSE-PMT 2006]
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a) L2, T and LT2
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b) LT2, LT and L
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c) L, LT and T2
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d) LT-2, L and T
Explanation
Dimensions at should be of velocity Thus a[T] = LT-1 [a] = LT-2 Dimension of C should be the dimension of time as two physical quantity of same dimension can be added ) so dimension of c=T Dimension of b /(t+c) should have dimension of velocity b/ [T] = L T-1 ∴ b T-1 = LT-1 so b = L Answer: (d)
Q.13
Which one of the following groups have quantities that do not have the same dimensions? [ CBSE-PMT 2001]
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a) pressure, stress
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b) velocity, speed
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c) force and impulse
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d) work and energy
Explanation
Force has dimension [ MLT-2] While impulse is force × time Dimensions of impulse = [MLT-1 Answer: (c)
Q.14
Which of the following is dimensional constant? [ CBSE-PMT 1995]
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a) Refractive Index
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b) Poisson Ratio
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c) Relative density
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d) Gravitational constant
Explanation
A quantity which has dimensions and a constant value is called dimensional constant. therefore, gravitational constant(G) is dimensional constant Answer:(d)
Q.15
In a vernier calliper N divisions of vernier scale coincides with (N-1) division of main scale ( in which length of one division is 1mm). The least count of the instrument should be ..[ CBSE-PMT 1994]
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a) N
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b) N-1
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c) 1/10N
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d) 1/(N-1)
Explanation
Least count = 1 MSD - 1 VSD MSD= is main scale division VSD= vernier scale division Now N VSD = (N-1)MSD (given) ∴ 1 VSD = (N-1) / N MSD = (1-1/N) MSD Least count = 1MSD - (1-1/N) MSD = (1/N)MSD Now 1 MSD = (1/10)cm ( given Main Scale division =1 mm = (1/10) cm) ∴ Least count =(1/N)(1/10) = 1/10N Answer: (c)
Q.16
A certain body weights 22.42 gm and has a measured volume of 4.7cc. The possible error in the measurement of mass and volume are 0.01gm and 0.1cc. The maximum error in the density will be .. [ CBSE-PMT 1991]
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a) 22%
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b) 2%
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c) 0.2%
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d) 0.02%
Explanation
density d = mass (M) / Volume (V) Answer: (b)
Q.17
The percentage error in the measurement of mass and speed are 2% and 3% respectively. The error i kinetic energy obtained by measuring mass and speed will be.. [ CBSE PMT 1995]
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a) 12%
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b) 10%
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c) 8%
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d) 2%
Explanation
Percentage error in mass Percentage error in speed Kinetic energy = ½ mV2 ∴ Error in measurement of Kinetic Energy = (Δm /m) + 2( ΔV/ V) Error in measurement of Kinetic energy = (2/100) +2(3/100) = 8/100 % Error = 8% Answer: (c)
Q.18
the density of 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.. [ BSE-PMT 1996]
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a) 7%
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b) 9%
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c) 12%
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d) 13%
Explanation
density d = mass(M) / volume (v) d = M / L3 Now relative error ∴ %error in density = %error in mass 9 %error in volume %error in density = 4+ 3(3) = 13% Answer:(d)
Q.19
the dimensions of Planck's constant are same as.. [ CBSE-PMT 201]
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a) Energy
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b) power
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c) momentum
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d) angular momentum
Explanation
We know that E = hν h = E / ν [h] = [ML2T-2 ] / T -1 [h] = [ML2T-1] Dimension of angular momentum = Iω Angular momentum = [ML2][T-1] Angular momentum = [ML2T-1] Answer: (d)
Q.20
Of the following quantities, which one has dimension different from the remaining three? [ CBSE-PMT 1989]
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a) Energy per unit volume
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b) Force per unit area
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c) Product of voltage and charge per unit volume
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d) Angular momentum
Explanation
For angular momentum, the dimensional formula is ML2T-1. For other three it is [ ML-1T-2] Answer: (d)
Q.21
In a particular system, the unit of length , mass and time are chosen to be 10cm, 10g and 0.1s respectively. The unit of force in this system will be equivalent to [ CBSE-PMT 1997]
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a) 0.1N
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b) 1N
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c) 10N
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d) 100N
Explanation
Dimensional formula for force F = MLT-2 1N = (10-2kg) ( 10-1)(10-1)-2 F = 10NEW UNITS of FORCE ∴ 1 NEW UNIT OF FORCE = 0.1N Answer: (a)
Q.22
The time dependence of physical quantity 'p' is given by p = poexp(-αt2), where α is a constant and t is the time. The constant α .... [CBSE-PMT 1993]
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a) is dimensionless
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b) has dimensions T-2
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c) has dimensions T2
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d) has dimensions of p
Explanation
Answer:(b)
Q.23
Dimension of resistance in an electric circuit in terms of dimensions of mass M, of length L, of time T and of current I, would be.. [ CBSE PMT 2007]
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a) ML2T-2
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b) ML2T-1I-1
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c) ML2T-3I-2
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d) ML2T-3I-1
Explanation
resistance R = V/I But V = Work / charge = Work / It ( I is current ,t is time) Thus R = Work / (I×It) = Work / (I2t) Dimensions of Work = ML2T-2 Dimensions of R = [ ML2T-2] / (I2T) [R] = [ ML2T-3I-2 ] Answer: (c)
Q.24
The dimension of ½ εo E2 ( ε0 is permittivity of free space, E is electric field ) is .. [ IIT 2000]
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a) MLT-1
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b) ML2T-2
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c) ML-1T-2
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d) ML2T-1
Explanation
Here given equation is for energy stored per unit volume in capacitor thus dimension will be = Energy / Volume dimension = ML2T-2 / L3 = ML-1T-2 Answer: (c)
Q.25
Which of the following set have different dimensions [ IIT 2005]
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a) Pressure, Youg's Modulus, Stress
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b) EMF, Potential difference
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c) Heat , Work done , Energy
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d) Dipole moment, Electric flux, Electric field
Explanation
Electric flux Φ = E ⋅S ∴ Φ ≠ E Answer: (d)
Q.26
A cube has a side of length 1.2×10-Calculate its volume .. [ CBSE-PMT 2003]
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a) 1.7×10-6 m3
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b) 1.73×10-6 m3
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c) 1.70×10-6 m3
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d) 1.732×10-6 m3
Explanation
V = l3 V = (1.2×10-2)3 V = 1.7×10-6 m3 NOTE: l has two significant figures. Hence V will also have two significant figures Answer:(a)
Q.27
Which of the following is the dimensional formula for the energy per unit area per sond
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a) ML0T0
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b) ML0T-3
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c) ML2T-1
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d) MT-2
Explanation
= Energy/ ( Area × time) = [ML2T-2 / [L2] [T] = ML0T-3 Answer: (b)
Q.28
Identify the pair whose dimensions are equal [ AIEE 2002]
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a) torque and work
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b) stress and energy
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c) force and stress
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d) force and work
Explanation
Torque = F r sinθ W = Fr Thus have same dimensional formula Answer: (a)
Q.29
The dimension of magnetic field in M,L,T, and C(coulomb) is given as .. [ AIEE 2008]
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a) MLT-1C-1
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b) MT2C-2
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c) MT-1C-1
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d) MT-2C-1
Explanation
We know that F = qvB B = F/qv Answer: (c)
Q.30
A quantity is given by Where εo is the permittivity of free space, L is the length, ΔV is a potential difference and Δt is a time interval. the dimensional formula for X is the same as that of .. [ IIT 2001]
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a) resistance
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b) charge
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c) voltage
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d) current
Explanation
Dimensionally εoL = C , C is capacitance Dimensionally CΔV is Q here Q is charge Now Q / Δ t = I , here I is current Answer:(d)
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