Given below are two statements :
$Statement$ $(I)$ : Planck's constant and angular momentum have same dimensions.
$Statement$ $(II)$ : Linear momentum and moment of force have same dimensions.
In the light of the above statements, choose the correct answer from the options given below :
Statement $I$ is true but Statement $II$ is false
Both Statement $I$ and Statement $II$ are false
Both Statement $I$ and Statement $II$ are true
Statement $I$ is false but Statement $II$ is true
In a typical combustion engine the work done by a gas molecule is given $W =\alpha^{2} \beta e ^{\frac{-\beta x ^{2}}{ KT }}$, where $x$ is the displacement, $k$ is the Boltzmann constant and $T$ is the temperature. If $\alpha$ and $\beta$ are constants, dimensions of $\alpha$ will be
If $R$ and $L$ represent respectively resistance and self inductance, which of the following combinations has the dimensions of frequency
Identify the pair of physical quantities which have different dimensions
Time $(T)$, velocity $(C)$ and angular momentum $(h)$ are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be
If $R , X _{ L }$. and $X _{ C }$ represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless: