Question

A block is resting on a piston which executes simple harmonic motion with a period $2.0$s. The maximum velocity of the piston, at an amplitude just sufficient for the block to separate from the piston is?

• A. $1.57$ $m{s}^{-1}$
• B. $3.12$ $m{s}^{-1}$
• C. $2.0$ $m{s}^{-1}$
• D. $6.42$ $m{s}^{-1}$

Answer 1

The correct option is B $3.12$ $m{s}^{-1}$

Maximum acceleration at which block separate :

$a_{max}=g$

${\omega }^{2}A=g$

$A=\frac{g}{{\omega }^2}$

$=\frac{g}{{\left(\frac{2\pi }{T}\right)}^2}$

$=\frac{g{T}^2}{4{\pi }^2}$

Maximum velocity of the piston :

$V_{max}=\omega A$

$=\frac{2\pi }{T}\times \frac{g{T}^2}{4{\pi }^2}$

$=\frac{gT}{2\pi }$

$=\frac{9.8\times 2}{2\pi }$

$=3.1m/s$