A block is resting on a piston which executes simple harmonic motion in vertical plain with a period of `2.0s` in vertical plane at an amplitude just sufficient for the block to separate from the piston. The maximum velocity of the piston is

Options

A. `(5)/(pi)(m)/(s)`
B. `(10)/(pi)(m)/(s)`
C. `(pi)/(2)(m)/(s)`
D. `(20)/(pi)(m)/(s)`

Answer

B

Explanation

The situation when the block is just below the mean position is shown Fig. the restoring forces acting on the piston cause a normal reaction F to act on the block. For the block to separate `Fgemg`
i.e, `momega^2Agemg`
(where `omega=` angular frequency and `A=`amplitude)
or `Age(g)/(omega^2)=(g)/(((2pi)/(T))^2)` or `Age(gT^2)/(4pi^2)`
Now, the maximum velocity `v_(max)` at that instant `=omegaA`
`v_(max)=((2pi)/(T))((gT^2)/(4pi^2))=(10)/(pi)(m)/(s^2)`