Question

Statement I: The given equation $x=x_{0}+u_{0}t+\frac{1}{2}at^{2}$ 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.
Statement II: Dimensional analysis can be used for checking the dimensional consistency or homogeneity of the equation

• A. If both statement I and statement II are true and statement II is the correct explanation of statement I.
• B. If both statement I and statement II are true but statement II is not the correct explanation of statement I.
• C. If statement I is true but statement II is false.
• D. If both statement I and statement II are false

Answer 1

Answer: (A)

Given equation:
$x=x_{0}+u_{0}t+\frac{1}{2}at^{2}$
The dimensions of each term may be written as
$\left[x\right]=\left[L\right]$
$\left[x_{0}\right]=\left[L\right]$
$\left[u_{0}t\right]=\left[LT^{-1}\right]\left[T\right]=\left[L\right]$
$\left[\left(\frac{1}{2}\right)at^{2}\right]=\left[LT^{-2}\right]\left[T^{2}\right]=\left[L\right]$
As each tern 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