A particle starts sliding down a friction-less plane. if $S_n$ is the distance traveled by it from $n-1$ seconds to $n$ seconds, the ratio $S_n/S_(n+1)$ is ?

Question

options :-
1. 2n-1/2n+1
2. 2n+1/2n
3. 2n/2n+1
4. 2n+1/2n-1

please answer with full explanation

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Answer 1 · 2017-08-05T14:26:46

Let $a$ be the acceleration of sliding. The initial velocity of the particle $u=0$
So the distance traversed during $nth$ sec

$S_n=u+1/2a(2n-1)=1/2a(2n-1)$

And the distance traversed during $(n+1)th$ sec

$S_(n+1)=u+1/2a(2n+2-1)=1/2a(2n+1)$

Hence the ratio

$S_n/S_(n+1)=(1/2a(2n-1))/(1/2a(2n+1))=(2n-1)/(2n+1)$