1.

The time period of a particle in simple harmonic motion is 8 second. At t = 0 it is at the mean position. The ratio of the distances travelled by it in the first and second is :

Answer»

`1//2`
`1//(sqrt(2)-1)`
`1//sqrt(2)`
`1//sqrt(3)`.

Solution :`y=R sin omega t`
`:. Y_(1)=r sin omega xx 1` and `y_(2)=r sin omega xx2`.
`:.""(y_(1))/(y_(2))=(sinomega)/(sin 2omega)=(1)/(2 cos omega)=(1)/(2.cos""(2PI)/(T))=(1)/(2 cos((2pi)/(8)))`
`:.""(y_(1))/(y_(2))=(1)/(sqrt(2)):.y_(2)=sqrt(2)y_(1)`
`:.` Distance coveredin `2"nd"=y_(2)-y_(1)=sqrt(2)y_(1)-y_(1)`
`=(sqrt(2)-1)y_(1)`
`:.` ratio of distances covered in Ist SECOND and 2ND second `=(1)/(sqrt(2)-1)`
Correctchoiceis (b).


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