A small block slides down on a smooth inclined plane, starting from rest at time $t = 0$. Let $S_n$ be the dis

Question

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 $\frac{S_n}{S_{n+1}}$ is

Accepted Answer

Let $	heta$ be the inclination of the inclined plane, acceleration $a = g \sin 	heta$. $S_n = u + \frac{a}{2}(2n-1)$. With $u=0$, $S_n = \frac{g \sin 	heta}{2}(2n-1)$. Similarly, $S_{n+1} = \frac{g \sin 	heta}{2}(2(n+1)-1) = \frac{g \sin 	heta}{2}(2n+1)$. Thus, $\frac{S_n}{S_{n+1}} = \frac{2n-1}{2n+1}$.

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