In a measurement,it is asked to find the modulus of elasticity per unit torque applied on the system. The measured quantity has the dimension of $[M^a L^b T^c]$. If $b = 3$,the value of $c$ is . . . . . . .

If $y$ represents pressure and $x$ represents velocity gradient,then the dimensions of $\frac{d^2 y}{d x^2}$ are

If $C$ is the velocity of light,$h$ is Planck's constant,and $G$ is the gravitational constant,and these are taken as fundamental quantities,then the dimensional formula of mass is:

In a system,the unit of mass is $A \,kg$,length is $B \,m$,and time is $C \,s$. Then,the value of $10 \,N$ in this system is:

If speed $V$,area $A$,and force $F$ are chosen as fundamental units,then the dimension of Young's modulus will be:

An expression for a dimensionless quantity $P$ is given by $P = \frac{\alpha}{\beta} \log_{e} \left( \frac{kt}{\beta x} \right)$,where $\alpha$ and $\beta$ are constants,$x$ is distance,$k$ is the Boltzmann constant,and $t$ is the temperature. Then the dimensions of $\alpha$ will be: