Question

Assertion :The given equation $x=x_0+u_{0}t+\frac{1}{2}a{t}^2$ is dimensionally 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 checking the dimensional consistency or homogeneity of the equation.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Given equation: $x=x_0+u_{0}t+\frac{1}{2}a{t}^2$.
The dimensions of each term may be written as
$\left[x\right]=\left[L\right];\left[x_0\right]=\left[L\right];\left[u_{0}t\right]=\left[L{T}^{-1}\right]\left[T\right]=\left[L\right]\left[\left(\frac{1}{2}\right)a{t}^2\right]=\left[L{Y}^{-2}\right]\left[T^2\right]=\left[L\right]$
As each term on the right hand side of this equation has the same dimension as left hand side of the equation, hence this equation is dimensionally correct.