Question

With usual notation, the following equation, said to give the distance covered in the $n^{th}$ second i.e., $S_n=u+a\frac{(2n-1)}{2}$ is :

• A. numerically correct
• B. dimensionally correct
• C. both dimensionally and numerically correct
• D. neither numerically nor dimensionally correct

Answer 1

Answer: (C)

both dimensionally and numerically correct

The given equation is the equation for the distance covered by a body in $n^{th}$ second of its motion.

$S_n=u+a\frac{(2n-1)}{2}$

Here, $u$ is the initial velocity, $a$ is the acceleration of the body and $n$ is the second in which the distance is covered.

The dimension of $S_n$ will be $\left[L{T}^{-1}\right]$ as it is the distance covered in 1 sec.

Substitute the dimensions in the equation.

$\left[L{T}^{-1}\right]=\left[L{T}^{-1}\right]+\left[L{T}^{-2}\right]\left[T\right]$

$\left[L{T}^{-1}\right]=\left[L{T}^{-1}\right]$

Hence, the above equation is dimensionally & numerically correct.