What is the dimension of the ratio of Planck's constant $(h)$ to the moment of inertia $(I)$?

  • A
    Frequency
  • B
    Velocity
  • C
    Angular momentum
  • D
    Time

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If $L$ and $R$ are respectively the inductance and resistance,then the dimensions of $\frac{L}{R}$ will be

Let the inductance and resistance be denoted by $L$ and $R$ respectively. The dimensions of $\left(\frac{L}{R}\right)$ are

Match List-$I$ with List-$II$:
List-$I$List-$II$
$(a)$ $h$ (Planck's constant)$(i)$ $[M L T^{-1}]$
$(b)$ $E$ (kinetic energy)$(ii)$ $[M L^2 T^{-1}]$
$(c)$ $V$ (electric potential)$(iii)$ $[M L^2 T^{-2}]$
$(d)$ $P$ (linear momentum)$(iv)$ $[M L^2 I^{-1} T^{-3}]$

Choose the correct answer from the options given below:

The position of a particle at time $t$ is given by the equation $x(t) = \frac{v_0}{A}(1 - e^{-At})$, where $v_0$ is a constant and $A > 0$. The dimensions of $v_0$ and $A$ respectively are:

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