Question

Snth=u + ( a / 2 )(2n-1) Check whether this equation is dimensionally correct or not.

Answer 1

The equation given in the question is -

                             $S_{nth} =u+\frac{a}{2} [2n-1]$

We are asked to prove it as per  dimensional analysis.

Here, Snth is the distance travelled by a particle between n and n-1  seconds.

u and a stands for initial velocity and acceleration.' n' stands for time.

As per the principle of homogeneity, every term given in an equation must have same dimension.

Here, the dimension of first term is -

                                             $[S_{nth} ]=[M^{0} L^{1} T^{-1}]$

The dimension of second term is -

                                             $[u]=\ [M^{0} L^{1} T^{-1}]$

                                                    $=M^{0} L^{1} T^{-1}$

The dimension of the third term is -

                                             $\frac{a}{2} [2n-1]=M^{0} L^{1} T^{-1}$

Here, all the terms have same dimension. Hence, the equation is dimensionally correct.