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If a spring has time period T, and is cu...

If a spring has time period T, and is cut into (n) equal parts, then the time period of each part will be.

A

`Tsqrt(n)`

B

`(T)/(sqrt(n))`

C

`nT`

D

`T`

Text Solution

Verified by Experts

The correct Answer is:
B
Time period of a mass loaded spring
`T = 2pisqrt((m)/(k))` So `T prop (l)/(sqrt(k)) "….."(i)`
Spring constant (k) is inversely proportional to the length of the spring i.e.,
`k prop 1/l`
`(k_("complete spring"))/(k_("cut spring")) = ((1//l))/((l/(l//n))) = l/n`
`rArr k_("cut spring") = n(k_("complete spring"))`
`rArr (T_("cut spring"))/(T_("complete spring")) = sqrt((k_("complete spring"))/(k_("cut of spring"))) = (1)/(sqrt(n))` [From (i)
`rArr T_("cut spring") = (T_("complete spring"))/(sqrt(n))`
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