If the unit of force is $1 \,kN$,the unit of length is $1 \,km$,and the unit of time is $100 \,s$,what will be the unit of mass in $kg$?

The equation of a circle is given by $x^2+y^2=a^2$,where $a$ is the radius. If the equation is modified to change the origin to a point other than $(0,0)$,find the correct dimensions of $A$ and $B$ in the new equation: $(x-At)^2+(y-\frac{t}{B})^2=a^2$. The dimensions of $t$ are given as $[T^{-1}]$.

$A$ physical quantity obtained from the ratio of the coefficient of thermal conductivity to the universal gravitational constant has a dimensional formula $[M^{2a} L^{4b} T^{2c} K^d]$. Then the value of $\frac{a+b}{c+b}-d$ is

The potential energy of a particle varies with distance $x$ from a fixed origin as $U = \frac{A\sqrt{x}}{x^2 + B}$,where $A$ and $B$ are dimensional constants. Find the dimensional formula for $A/B$.

If $A, B$ and $C$ are three different physical quantities with different dimensional formulae, then the combination which can never give a proper physical quantity is

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