Kinematics 2 Question 5
7. A small block slides without friction down an inclined plane starting from rest. Let $s _n$ be the distance travelled from $t=n-1$ to $t=n$. Then, $\frac{s _n}{s _{n+1}}$ is
(a) $\frac{2 n-1}{2 n}$
(b) $\frac{2 n+1}{2 n-1}$
(c) $\frac{2 n-1}{2 n+1}$
(d) $\frac{2 n}{2 n+1}$
(2004, 2M)
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Answer:
Correct Answer: 7. (c)
Solution:
- Distance travelled in $n^{\text {th }}$ second is, $s _n=u+a n-\frac{1}{2} a$
Given, $u=0$
$$ \therefore \quad \frac{s _n}{s _{n+1}}=\frac{a n-\frac{1}{2} a}{a(n+1)-\frac{1}{2} a}=\frac{2 n-1}{2 n+1} $$
$\therefore$ Correct option is (c).
