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Units and Measurements Test - 23

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Units and Measurements Test - 23
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Weekly Quiz Competition
  • Question 1
    1 / -0
    The dimensional formula M1L3T2{ M }^{ -1 }{ L }^{ 3 }{ T }^{ -2 } refers to :
    Solution
    Force =MLT2=MLT^{-2}
    Power =ML2T3=ML^{2}T^{-3}
    Energy =ML2T2=ML^{2}T^{-2}
    Gravitation constant 
    =M1L3T2=M^{-1}L^{3}T^{-2}
  • Question 2
    1 / -0
    The dimensional formula for angular velocity is:
    Solution

    $$Angular \ velocity,

    W=\dfrac{1}{Time}=T^{-1}M^{0}L^{0}$$

  • Question 3
    1 / -0
    The dimensions of calorie are :
    Solution
    Its a unit of energy whose dimensions can be calculated as F.dr=MLT2L=ML2T2F.dr=MLT^{-2}L=ML^2T^{-2}
  • Question 4
    1 / -0
    The dimensions of resistivity in terms of M, L, T and Q, where Q stands for the dimensions of charge is :
    Solution
    R=ρlAR=\dfrac{\rho l}{A}
    Power =I2R=I^2R
    Dimension of R is ML2T1Q2T2=ML2TQ2\dfrac{ML^2{T}^{-1}}{Q^2T^{-2}}=ML^2TQ^{-2}
    Now by equation, ρ=RAL=ML2TQ2L=ML3TQ2\rho=\dfrac{RA}{L}=ML^2TQ^{-2}L=ML^3TQ^{-2}
    Hence, option A is correct.
  • Question 5
    1 / -0
    Which of the following pair does not have the same dimensions?
    Solution
    Moment of inertia =mr2=ML2={mr}^{2}={ML}^{2}
    Torque =M1L2T2=M^{1}L^{2}T^{-2}
    Linear momentum =mv=MLT1=mv=MLT^{-1}
    Impulse =MLT1=MLT^{-1}
    Angular momentum 
    =ML2T1=ML^{2}T^{-1}
    Planks constant=ML2T2=ML^{2}T^{-2}
    Work =ML2T2=ML^{2}T^{-2}
    Internal Energy 
    =ML2T2=ML^{2}T^{-2}
    Hence, option A is correct.
  • Question 6
    1 / -0
    The dimensional formula for impulse is:
    Solution

    $$Impulse=force\times
    time=ML^{1}T^{-2}\times T^{1}$$=MLT1=MLT^{-1}

  • Question 7
    1 / -0
    The SI unit of a physical quantity having the dimensional formula of ML0T2A1{ ML }^{ 0 }{ T }^{ -2 }{ A }^{ -1 } is:
    Solution
    ampamp m2=A1L2m^{2}=A^{1}L^{2}
    ampamp metermeter=A1L1=A^{1}L^{1}
    weberweber =ML2A1T2=ML^{2}A^{-1}T^{-2}
    AA\rightarrow ampere
    TeslaTesla 
    =M1L0T2A1=M^{1}L^{0}T^{-2}A^{-1}
    Hence, option A is correct answer.
  • Question 8
    1 / -0
    According to theory of significant figures the value of 3.0\sqrt { 3.0 } is:
    Solution
    3.0=1.732\sqrt{3.0}=1.732
    Since 3.0 has 2 significant figure,
    So, our answer should have 2 significant figure
    i.e. 1.7321.71.732\approx 1.7
  • Question 9
    1 / -0
    The number of significant figures in the numbers 672.9672.9 and 2.520×1072.520\times { 10 }^{ 7 } are :
    Solution

    672.96,7,2,9672.9 \rightarrow 6, 7, 2, 9 \rightarrow 4 significant digits since all non zero digits are significant.
    2.520×1072,5,2,042.520\times 10^{7} \rightarrow 2, 5, 2, 0 \rightarrow 4 significant digits, since all the zero on the right side of last non zero digit in the decimal part are significant.

  • Question 10
    1 / -0
    The dimensional formula for Areal velocity is :
    Solution
    It is the area covered per unit time dAdt=L2T1\dfrac{dA}{dt}=L^2T^{-1}
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