Question

In a spring-block system, length of the spring is increased by 5%. The time period will ____________.

पर्याय

• increase by 5%.

• increase by 2.5%.

• decrease by 10%

• decrease by 2.5%

Answer 1

In a spring-block system, length of the spring is increased by 5%. The time period will increase by 2.5%.

Explanation:

`"k" prop 1/"length of spring" "and"  "T" = 2pi sqrt(m/k) Rightarrow "T" prop 1/sqrtk`

`therefore "T" prop sqrt"length of spring"  or  "T" prop sqrtL`

differentiating and multiplying by 100,

`(dT)/T xx 100 = 1/2 ((dL)/L) xx 100`

`therefore "% change in T" = 1/2  "(% change in length)"`

`= 1/2 xx 5% = 2.5%`

As length is increased, change in length is positive. Hence, time period will increase by 2.5%.