A second's pendulum is taken from a place where `g=9.8 ms^(-2)` to a place where `g=9.7 ms^(-2)` .How would its length be changed in order that its time period remains unaffected ?

Explanation

`T=2pisqrt((l)/(g))=2pisqrt((l^('))/(g^('))) or l^(')=(lg^('))/(g)=(lxx9.7)/(9.8)`
Decrease in length `=l-l^(')=l(1-(9.7)/(9.8))=(0.1)/(9.8)l`
Here, `l=(T^(2)g)/(4pi^(2))=(2^(2)xx9.8)/(4xx(22//7)^(2))=0.992`
`:. l-l^(')=(0.1)/(9.8)xx0.992=0.0101m`