Question

A force F is given by F = at + bt?, where 't' is
time. What are the dimensions of a and b?
a) [M'L'T-1] and [M'L'Tº]
b) [M'L'T-3) amd [M'L'T41
c) [M'L'T'] and [M'L'T']
d) [M'L-PT'] and [M'L'T-4)​

Answer 1

Is that bt^2? If so then,

F = ma so the unit is kgm/s^2

Also given,

F = at + bt^2 where t is time so,

at = kgm/s^2 and bt^2 = kgm/s^2 because by the laws of dimensions only units with equal dimensions can be added/ equated.

So,

If at = kgm/s^2

then a = kgm/s^3

and if bt^2 = kgm/s^2

then b = kgm/s^4

Therefore,

a= kgm/s^3 and b= kgm/s^4

So the dimensions are: a= M'L'T-3

                                       b= M'L'T-4

Hope it helps!

Answer 2

Explanation:

A force F is given by F=at+bt2, where t is time. The dimensions of a and b are: A. [MLT−3]and[MLT−4]. B . [MLT−4]and[MLT−3]. C. [MLT−1]and[MLT−2]. D ...