1.

Abody of mass `m` is suspended from two light springs of force constant `k_(1)` and `k_(2)(k_(1))` separately. The periods of vertical oscillations are `T_(1)` and `T_(2)` respectively. Now the same body is suspended from the same two springs which are first connected in series and then in parallel. The period of vertical oscillations are `T_(s)` and `T_(p)` respectively, thenA. `T_(p)ltT_(1)ltT_(2)ltT_(s)`B. `T_(s)^(2)=T_(1)^(2)+T_(2)^(2)`C. `sqrt(T_(s))=sqrt(T_(1))+sqrt(T_(2))`D. `(1)/(T_(p)^(2))=(1)/(T_(1)^(2))+(1)/(T_(2)^(2))`

Answer» Correct Answer - A::B::D
`T_(1)=2pisqrt((m)/(k_(1))), T_(2)=2pisqrt((m)/(k_(2)))`
`T_(s)=2pisqrt((m)/((k_(1)k_(2))//(k_(1)=k_(2))))`
`T_(p)=2pisqrt((m)/((k_(1)+k_(2))))`
From above we note that `T_(s)gtT_(2)gtt_(1)gtT_(p),i.e.,` option (a) is correct.
`(1)/(T_(p)^(2))=(k_(1)+k_(2))/(4pi^(2)m)=(k_(1))/(4pi^(2)m)+(k_(2))/(4pi^(2)m)`
`=(1)/(T_(1)^(2))+(1)/(T_(2)^(2)),i.e.,` option (d) is correct.
`T_(s)^(2)=(4pi^(2)m(k_(1)+k_(2)))/(k_(1)k_(2))=(4pi^(2)m)/(k_(2))+(4pi^(2)m)/(k_(1))`
`=T_(2)^(2)+T_(1)^(2), i.e.,` option (b) is correct.


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