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A box is placed on a smototh plane end i...

A box is placed on a smototh plane end it is free to move. A single penldulum is attached in the block. Find its time period.

Text Solution

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Let `F_(p) =` Pseudo force
For equilibrium position
`Tsinalpha + F_(P) = mgsintheta`
`Tsinalpha + ma = mgsintheta`
since `a = gsintheta`
`Tsinalpha + mgsintheta = mgsintheta`
`Tsinalpha = 0`
`:. alpha = 0`

Hence in equilibrium position the string is perpendicular to incline plane.
Therefore effective `'g'` is
`g_(eff) = gcos theta`
Time period
`T = 2pisqrt((l)/(g_(eff))`
`T = 2pisqrt((l)/(gcostheta))` Ans.
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