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NEET-XII-Physics

01: Introduction to Physics

by HC Verma - page 2
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  • #2
    Find the dimensions of (a) angular speed ω, (b) angular acceleration α, (c) torque
    τand (d) moment of interia I = ``mr^2``.
    The symbols have standard meanings. (a) angular speed ω, (b) angular acceleration α, (c) torque
    τand (d) moment of interia I = ``mr^2``.
    The symbols have standard meanings.
    Ans : (a) Dimensions of angular speed, `` \, \mathrm{\omega }=\frac{\, \mathrm{\theta }}{t}=\left[{\, \mathrm{M}}^{0}{\, \mathrm{L}}^{0}{\, \mathrm{T}}^{-1}\right]`` (b) Angular acceleration, `` \, \mathrm{\alpha }=\frac{\, \mathrm{\omega }}{t}\phantom{\rule{0ex}{0ex}}``
    Here, ω = [``M^0L^0T^{-1}```] and t = [T]
    So, dimensions of angular acceleration = [``M^0L^0T^{-2}``] (c) Torque, τ =Frsin`` \theta ``
    Here, F = [MLT-2] and r = [L]
    So, dimensions of torque = [ML2T-2] (d) Moment of inertia =`` mr^2``
    Here, m = [M] and`` r^2`` = [``L^2``]
    So, dimensions of moment of inertia = [``ML^2T^0``] (a) Dimensions of angular speed, `` \, \mathrm{\omega }=\frac{\, \mathrm{\theta }}{t}=\left[{\, \mathrm{M}}^{0}{\, \mathrm{L}}^{0}{\, \mathrm{T}}^{-1}\right]`` (b) Angular acceleration, `` \, \mathrm{\alpha }=\frac{\, \mathrm{\omega }}{t}\phantom{\rule{0ex}{0ex}}``
    Here, ω = [``M^0L^0T^{-1}```] and t = [T]
    So, dimensions of angular acceleration = [``M^0L^0T^{-2}``] (c) Torque, τ =Frsin`` \theta ``
    Here, F = [MLT-2] and r = [L]
    So, dimensions of torque = [ML2T-2] (d) Moment of inertia =`` mr^2``
    Here, m = [M] and`` r^2`` = [``L^2``]
    So, dimensions of moment of inertia = [``ML^2T^0``]
  • #2-a
    angular speed ω,
    Ans : Dimensions of angular speed, `` \, \mathrm{\omega }=\frac{\, \mathrm{\theta }}{t}=\left[{\, \mathrm{M}}^{0}{\, \mathrm{L}}^{0}{\, \mathrm{T}}^{-1}\right]``
  • #2-b
    angular acceleration α,
    Ans : Angular acceleration, `` \, \mathrm{\alpha }=\frac{\, \mathrm{\omega }}{t}\phantom{\rule{0ex}{0ex}}``
    Here, ω = [``M^0L^0T^{-1}```] and t = [T]
    So, dimensions of angular acceleration = [``M^0L^0T^{-2}``]
  • #2-c
    torque
    τand
    Ans : Torque, τ =Frsin`` \theta ``
    Here, F = [MLT-2] and r = [L]
    So, dimensions of torque = [ML2T-2]
  • #2-d
    moment of interia I = ``mr^2``.
    The symbols have standard meanings.
    Ans : Moment of inertia =`` mr^2``
    Here, m = [M] and`` r^2`` = [``L^2``]
    So, dimensions of moment of inertia = [``ML^2T^0``]