00:01
The question says an equation of motion is given by x is equal to a t square plus b g plus c, where a, b, c are unknown constant and unknown variables if x measures the position and t measures the time.
00:14
So we have to find the dimensions of a, b and c.
00:17
So this question is purely based on the concept of the principle of homogeneity of dimension.
00:24
So principle of homogeneity of dimension says any physical quantity.
00:30
Any physical quantity will be any physical quantity will be dimensional correct will be dimensionally correct if the dimensions are same for all the terms present there for all the terms occurring on both sides.
01:20
This is known as principle of homogeneity.
01:24
Now to calculate the dimensions of a, what we have to do, x is equal to 80 square.
01:33
So, a is equal to x by t squared.
01:36
As we know that x is position so its dimension quantity is l and t is sign so the dimensions for a will be l t minus two similarly we will calculate the dimensions of b so dimensions of b will be equal to x is equal to b t is equal to b so dimensions of b will be will be lt minus 1...