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)#