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Springs of spring constant K,3K,9K,27K,…...

Springs of spring constant K,3K,9K,27K,….243K are connected in series. A mass M is attached to the last spring and the system is allowed to make oscillation. The time period will be

A

`2pisqrt((M)/(K))`

B

`2pisqrt((3M)/(2K))`

C

`(4pi)/(9)sqrt((91M)/(3K))`

D

`2pisqrt((4M)/(3K))`

Text Solution

Verified by Experts

C
`(1)/(K_(0))=(1)/(K)+(1)/(3K)+(1)/(9K)+.......+(1)/(243K)`
`:. K_(0)=(243K)/(364)`
`T=2pisqrt((m364)/(243K))=(4pi)/(9)sqrt((91M)/(3K))`
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