Home
Class 12
PHYSICS
Infinite springs with force constants k,...

Infinite springs with force constants k,2k, 4k and 8k … respectively are connected in series. What will be the effective force constant of springs, when `k=10N//m`

Text Solution

Verified by Experts

The correct Answer is:
1
As springs are connected in series , the equivalent value of the constand will be `(1)/(K)=(1)/(2)+(1)/(4)+(1)/(8)+(1)/(16)+(1)/(32)+`……….
`(1)/(K)=[1+(1)/(2^(1))+(1)/(2^(2))+(1)+(2^(3))+(1)/(2^(4))+…..]-1`
`(1)/(K)=[1+(1)/(1-(1)/(2))]-1=2-1=1`
`therefore K=1`
Promotional Banner

Similar Questions

Explore conceptually related problems

Infinite spring with force constants k, 2k, 4k, 8k ,……..respectively are connected in series. Calculate the effetive force constant of the spring.

Infinite springs with force constant k , 2k, 4k and 8 k .... respectively are connected in series. The effective force constant of the spring will b

Infinite springs with force constants k, 2k, 4k, 8k,….. respectively are connected in series to which mass 'm' is attched. The frequency of small oscillations is……..

A spring (spring constant=k) is cuttend into 4 equal parts and two parts are connected in parallel. What is the effective spring constant?

A spring of force constant k is cut into four equal parts. The force constant of each part will be

Two springs of spring constants K_(1) and K_(2) are joined in series. The effective spring constant of the combination is given by

As shown in the figure, two light springs of force constant k_(1) and k_(2) oscillate a block of mass m. Its effective force constant will be