In the equation $(P+\frac{a}{V^2})(V-b)=RT$,where $P$ is pressure,$V$ is volume,$T$ is temperature,$R$ is universal gas constant,and $a$ and $b$ are constants. The dimensions of $a$ are

Two quantities $A$ and $B$ have different dimensions. Which mathematical operation given below is physically meaningful?

$A$ small steel ball of radius $r$ is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity $\eta$. After some time,the velocity of the ball attains a constant value known as terminal velocity $v_T$. The terminal velocity depends on $(i)$ the mass of the ball $m$,$(ii)$ $\eta$,$(iii)$ $r$,and $(iv)$ acceleration due to gravity $g$. Which of the following relations is dimensionally correct?

Given that $v$ is the speed,$r$ is the radius,and $g$ is the acceleration due to gravity. Which of the following is dimensionless?

Young's modulus of elasticity $Y$ is expressed in terms of three derived quantities,namely,the gravitational constant $G$,Planck's constant $h$,and the speed of light $c$,as $Y = c^\alpha h^\beta G^\gamma$. Which of the following is the correct option?

With the usual notations,the following equation $S_t = u + \frac{1}{2}a(2t - 1)$ is