Units, Dimensions and Measurement
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Questions and Answers

What is the dimensional formula of angular momentum in terms of v, A, and F?

  • Fv²A⁻¹
  • FvA⁻¹
  • Fv³A⁻² (correct)
  • F²v²A⁻¹

    • What is the correct relation between the largest mass (m) that can be moved by a flowing river and the velocity (v), density (ρ) of river water, and acceleration due to gravity (g)?

  • m ∝ ρv⁶g
  • m ∝ ρv⁶g³ (correct)
  • m ∝ ²ρv⁴g³
  • m ∝ ρ²v⁴g²

    • What is the unit of acceleration due to gravity (g) in the given problem?

  • [LT⁻¹]
  • [LT⁻²] (correct)
  • [MLT⁻²]
  • [MLT⁻¹]

    • What is the unit of velocity (v) in the given problem?

    <p>[LT⁻¹]</p> Signup and view all the answers

    Which of the following is not a fundamental quantity in the given problem?

    <p>angular momentum</p> Signup and view all the answers

    What is the terminal velocity of a small steel ball in a viscous liquid?

    <p>The constant velocity of the ball after some time</p> Signup and view all the answers

    What determines the terminal velocity of a small steel ball in a viscous liquid?

    <p>The mass of the ball, coefficient of viscosity, radius, and acceleration due to gravity</p> Signup and view all the answers

    Which of the following has the dimension [ML⁻¹T⁻¹]?

    <p>Coefficient of viscosity</p> Signup and view all the answers

    What is the correct relation between terminal velocity and other physical quantities?

    <p>vT ∝ mg/ηr</p> Signup and view all the answers

    What is the purpose of dimensional analysis in the given problem?

    <p>To check the accuracy of the given formula</p> Signup and view all the answers

    If F2 = 1 in two systems of relations among velocity, acceleration, and force, then what can be inferred about the relation between F and v?

    <p>F α 2v1</p> Signup and view all the answers

    If M2 = α^3 M1 and L2 = α^2 L1, then what can be inferred about the relation between T2 and T1?

    <p>T2 = α^2 T1</p> Signup and view all the answers

    If a2 = αβ a1, then what can be inferred about the relation between v2 and v1?

    <p>v2 = αβ v1</p> Signup and view all the answers

    What is the relation between L2 and L1 in the given system?

    <p>L2 = α^2 L1</p> Signup and view all the answers

    What is the dimension of the coefficient of rigidity in the given problem?

    <p>[ML⁻¹T⁻¹]</p> Signup and view all the answers

    What is the correct dimension of the time period of the oscillating block?

    <p>[T]</p> Signup and view all the answers

    What is the dimension of the force applied to the block A?

    <p>[MLT⁻²]</p> Signup and view all the answers

    If the mass of the block A is increased by a factor of 2, what will be the effect on the time period of the oscillations?

    <p>The time period will increase by a factor of 2.</p> Signup and view all the answers

    What is the relation between the dimension of the length and the dimension of the time period?

    <p>The dimension of the length is square root of the dimension of the time period.</p> Signup and view all the answers

    What is the correct expression for the time period of the oscillating block?

    <p>T = 2π √(ML/η)</p> Signup and view all the answers

    If the coefficient of rigidity is increased by a factor of 2, what will be the effect on the time period of the oscillations?

    <p>The time period will decrease by a factor of 2.</p> Signup and view all the answers

    What is the dimension of the product ML in the given problem?

    <p>[ML⁺¹]</p> Signup and view all the answers

    What is the correct relation between the dimension of the mass and the dimension of the coefficient of rigidity?

    <p>[M] = [η][L]⁻¹</p> Signup and view all the answers

    What is the purpose of dimensional analysis in the given problem?

    <p>To check the accuracy of the given formulae.</p> Signup and view all the answers

    What is the primary purpose of significant figures in physics?

    <p>To indicate the precision of a measurement</p> Signup and view all the answers

    A physical quantity has a dimension of [ML^(-1)T^(-1)]. What can be said about the quantity?

    <p>It is a derived quantity</p> Signup and view all the answers

    What is the maximum number of physical quantities that can be used to derive a formula using dimensional analysis?

    <p>3</p> Signup and view all the answers

    What is the primary limitation of dimensional analysis?

    <p>It cannot be used to derive formulas involving more than 3 physical quantities</p> Signup and view all the answers

    What can be said about a formula that cannot be derived using dimensional analysis?

    <p>Its dimensional correctness can be checked using dimensional analysis</p> Signup and view all the answers

    What is the significance of a large number of significant figures in a measurement?

    <p>It indicates a high degree of precision in the measurement</p> Signup and view all the answers

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