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

Options

A. `Tsqrt(n)`
B. `(T)/(sqrt(n))`
C. `nT`
D. `T`

Answer

B

Explanation

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))`