The dimensions of universal gravitational constant are
${M^{ - 2}}{L^2}{T^{ - 2}}$
${M^{ - 1}}{L^3}{T^{ - 2}}$
$M{L^{ - 1}}{T^{ - 2}}$
$M{L^2}{T^{ - 2}}$
If $L$ denotes the inductance of an inductor through which a current $i$ is flowing, the dimensions of $L{I^2}$ are
Force $F$ is given in terms of time $t$ and distance $x$ by $F = a\, sin\, ct + b\, cos\, dx$, then the dimension of $a/b$ is
Dimensional formula for torque is
Sometimes it is convenient to construct a system of units so that all quantities can be expressed in terms of only one physical quantity. In one such system, dimensions of different quantities are given in terms of a quantity $X$ as follows: [position $]=\left[X^\alpha\right] ;[$ speed $]=\left[X^\beta\right]$; [acceleration $]=\left[X^{ p }\right]$; [linear momentum $]=\left[X^{ q }\right]$; [force $]=\left[X^{ I }\right]$. Then -
$(A)$ $\alpha+p=2 \beta$
$(B)$ $p+q-r=\beta$
$(C)$ $p-q+r=\alpha$
$(D)$ $p+q+r=\beta$
Turpentine oil is flowing through a tube of length $l$ and radius $r$. The pressure difference between the two ends of the tube is $P .$ The viscosity of oil is given by $\eta=\frac{P\left(r^{2}-x^{2}\right)}{4 v l}$ where $v$ is the velocity of oil at a distance $x$ from the axis of the tube. The dimensions of $\eta$ are