Assertion: The given equation `x = x_(0) + u_(0)t + (1)/(2) at^(2)` is dimensionsally correct, where x is the distance travelled by a particle in time t , initial position `x_(0) ` initial velocity `u_(0)` and uniform acceleration a is along the direction of motion.
Reason: Dimensional analysis can be used for cheking the dimensional consistency or homogenetly of the equation.

Options

A. If both assertion and reason are true and reason is the correct explation of assertion.
B. If both assertion but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If both assertion and reason are false.

Answer

a

Explanation

Given equation
`x = s_(0)+ u_(0)t + (1)/(2) at^(2)`
The dimensions of each term mey be written as
`[x] = [L]`
`[x_(0)] = [L]`
`[u_(0)t]= [LT^(-1)][T]= [L]`
`[((1)/(2)) at^(2)] = [LT^(-2)][T^(2)] = [L]`
As each term on the right hand side of the equation the same dimension as left hand side of the equal hence this equation id dimensionally correct.