2021 Laws of MotionMotion on an Inclined Plane Medium Question 1 of 2 in Motion on an Inclined Plane

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:

A $\frac{2n-1}{2n+1}$
B $\frac{2n+1}{2n-1}$
C $\frac{2n}{2n-1}$
D $\frac{2n-1}{2n}$

The answer is A.

Solution

Starting from rest with constant acceleration a, distance in the $n^{th}$ second: $S_n = \frac{a}{2}(2n - 1)$ $S_{n+1} = \frac{a}{2}(2(n+1) - 1) = \frac{a}{2}(2n + 1)$ $\frac{S_n}{S_{n+1}} = \frac{2n - 1}{2n + 1}$

Concept distance in the nth second

Motion on an Inclined Plane in past papers

2 questions from this chapter have appeared across 2 exam years.