The thrust developed by a rocket-motor is given by $$F = mv + A\left( {{P_1} - {P_2}} \right)$$ where $$m$$ is the mass of the gas ejected per unit time, $$v$$ is velocity of the gas, $$A$$ is area of cross-section of the nozzle, $${{P_1}}$$ and $${{P_2}}$$ are the pressures of the exhaust gas and surrounding atmosphere. The formula is dimensionally
A.
correct
B.
wrong
C.
sometimes wrong, sometimes correct
D.
Data is not adequate
Answer :
correct
Solution :
Use principle of homogeneity.
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-