$$E,m,J$$ and $$G$$ denote energy, mass, angular momentum and gravitational constant respectively, then the unit of $$\frac{{E{J^2}}}{{{m^5}{G^2}}}$$ is
A.
newton
B.
metre
C.
kilogram
D.
unitless
Answer :
unitless
Solution :
Unitless quantity.
Releted MCQ Question on Basic Physics >> Unit and Measurement
Releted Question 1
The dimension of $$\left( {\frac{1}{2}} \right){\varepsilon _0}{E^2}$$ ($${\varepsilon _0}$$ : permittivity of free space, $$E$$ electric field)
A quantity $$X$$ is given by $${\varepsilon _0}L\frac{{\Delta V}}{{\Delta t}}$$ where $${ \in _0}$$ is the permittivity of the free space, $$L$$ is a length, $$\Delta V$$ is a potential difference and $$\Delta t$$ is a time interval. The dimensional formula for $$X$$ is the same as that of-
Pressure depends on distance as, $$P = \frac{\alpha }{\beta }exp\left( { - \frac{{\alpha z}}{{k\theta }}} \right),$$ where $$\alpha ,$$ $$\beta $$ are constants, $$z$$ is distance, $$k$$ is Boltzman’s constant and $$\theta $$ is temperature. The dimension of $$\beta $$ are-