Q 11-02-009NEETNEET 2021Top questionMedium
A small block slides down on a smooth inclined plane, starting from rest at time $t = 0$. Let $S_n$ be the distance travelled by the block in the interval $t = n - 1$ to $t = n$. Then, the ratio $\dfrac{S_n}{S_{n+1}}$ is :
Answer: (C) $\dfrac{2n - 1}{2n + 1}$
Concept. From rest with constant acceleration $a$, the distance in the $n$th second is $S_n = \dfrac{a}{2}(2n - 1)$.
Step 1. Distance in the $n$th second.
$$S_n = \frac{a}{2}\left[n^2 - (n - 1)^2\right] = \frac{a}{2}(2n - 1)$$
Step 2. Ratio.
$$\frac{S_n}{S_{n+1}} = \frac{2n - 1}{2n + 1}$$
Answer. $\dfrac{2n - 1}{2n + 1}$ (Option C).
Solution by Sreeraj P, M.Sc Physics