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Question

A block is moving down a smooth inclined plane staring from rest at time t=0 let Sn be the distance travel by the block in the interval t = n - 1 to t = n. The ratio SnSn+1is

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Solution

Given that,

Sn be the distance travel by the block in the interval t = n-1 and t = n.

Then,

Applying second equation of motion,

Then,

s=ut+12at2....(I)

Since u = 0

At t = n-1

Now, put the value of t in equation (I)

s=0+12×a×(n1)2

s=a(n1)22

Now, At t = n

Put the value of t in equation (I)

s=12an2

Now, the difference

Sn=ss

Sn=12a(n2(n1)2)

Sn=12a(n2n21+2n)

Sn=12a(2n1)......(II)

Now, put n+1 in place of n in equation (II)

Sn+1=12a(1+2(n+1))

Sn+1=12a(2n+1)

Now, the ratio of Sn and Sn+1

SnSn+1=2n12n+1

Hence, the ratio of SnSn+1 is 2n12n+1.


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