The $SI$ unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be ..............
$\left[ ML ^{-1} T ^{-1}\right]$
$\left[ ML ^{-1} T ^{-2}\right]$
$\left[ ML ^{2} T ^{-1}\right]$
$\left[ M ^{-1} L ^{3} T ^{0}\right]$
A system has basic dimensions as density $[D]$, velocity $[V]$ and area $[A]$. The dimensional representation of force in this system is
A highly rigid cubical block $A$ of small mass $M$ and side $L$ is fixed rigidly onto another cubical block $B$ of the same dimensions and of low modulus of rigidity $\eta $ such that the lower face of $A$ completely covers the upper face of $B$. The lower face of $B$is rigidly held on a horizontal surface. A small force $F$ is applied perpendicular to one of the side faces of $A$. After the force is withdrawn block $A$ executes small oscillations. The time period of which is given by
If speed $(V)$, acceleration $(A)$ and force $(F)$ are considered as fundamental units, the dimension of Young’s modulus will be
The magnetic moment has dimensions of
$A, B, C$ and $D$ are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation $AD = C\, ln\, (BD)$ holds true. Then which of the combination is not a meaningful quantity ?