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Physics question involving function of time? Please help, this is urgent.?
The volume of an object as a function of time is V(t)=At^3, where A is some constant.Let L and T denote dimensions of length and time. Determine the dimension of the constant A?
multiple choice answers:
1. L^3 x T^3
2. L^2 / T
3. L / T
4. L^3 / T^3
5. L / T^3

Answer:
the correct option is 4.


Dimensional analysis:
basically there are three dimensions. 1) dimension of mass (M), 2) dimension of length (L) and dimension of time (T). and all other measurements are converted into these three dimension. as for example in the above question volume. the volume is the product of length, breadth and height which means three units of length. so the dimension of length is used three times i.e L^3. also if you want know about the dimension of force then you hav to break down the force in such a way that it contains either or all or any of the above three dimensions.(also nothing more than the above three)
okay lets find out the dimension of force which wil give a clear idea. first of all you must know all the basic formulae of the term of which you are going to find the dimension.
froce= mass *acceleration
=mass*velocity/ time (since, acceleration=velocity/time)
= mass* (distance/time)*1/time (since,velocity=distance/time)
where distance means lengtth. hence we converted force into mass length and time.
therefore the dimension of force is
= ML/T^2
=MLT^-2

Here is the trick. if u want to knw the dimension of any term then the unit of the term will help alot. As in above case the unit of volume is m^3 which says its dimension is L^3.
i hope its clear to you now. if you still have doubts you can always write to me. i will be more elaboreate.