1.

Two springs, of spring constants `k_(1)` and `K_(2)`, have equal highest velocities, when executing SHM. Then, the ratio of their amplitudes (given their masses are in the ratio `1:2`) will beA. `((k_(2))/(k_(1)))^(1//2)`B. `((k_(1))/(k_(2)))^(1//2)`C. `(k_(1))/(k_(2))`D. `k_(1)k_(2)`

Answer» Correct Answer - A
The angular frequency of spring is given by
`omega = sqrt((k)/(m)) prop sqrt(k)`
For equal maximum velocities, we have
`A_(1)omega_(1) = A_(2)omega_(2)`
or `(A_(1))/(A_(2))=(omega_(2))/(omega_(1))=sqrt((k_(2))/(k_(1)))=((k_(2))/(k_(1)))^((1)/(2))" "(because m = m_(1) = m_(2))`


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