In the equation $x = a + bt + ct^2$,where $x$ is in meters and $t$ is in seconds,find the units of $a, b,$ and $c$.

If the unit of force is $100\,N$,unit of length is $10\,m$ and unit of time is $100\,s$,what is the unit of mass in this system of units?

What is dimensional analysis? Write the limitations of dimensional analysis.

$A$ book with many printing errors contains four different formulas for the displacement $y$ of a particle undergoing a certain periodic motion:
$(a) \; y = a \sin \left(\frac{2 \pi t}{T}\right)$
$(b) \; y = a \sin v t$
$(c) \; y = \left(\frac{a}{T}\right) \sin \frac{t}{a}$
$(d) \; y = (a \sqrt{2}) \left(\sin \frac{2 \pi t}{T} + \cos \frac{2 \pi t}{T}\right)$
($a =$ maximum displacement of the particle,$v =$ speed of the particle,$T =$ time-period of motion). Rule out the wrong formulas on dimensional grounds.

What is the dimensional formula of $ab^{-1}$ in the equation $(P+\frac{a}{V^2})(V-b)=RT$,where letters have their usual meaning?

From the following,the quantity (constructed from the basic constants of nature) that has the dimensions of length,as well as the correct order of magnitude for a typical atomic size,is: