A block is resting on a piston which executes simple harmonic mot… - Vidyadip

MCQ

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 .......... $ms ^{-1}$

A
$1.57$
✓
$3.12$
C
$2.0$
D
$6.42$

✓

Answer

Correct option: B.

$3.12$

b
(b)

Period $(T)=2 \,s$

$\omega=\frac{2 \pi}{2}=\pi \,rad / s$

When block just represent from a piston, maximum acceleration must be equal to $g$.

$g=-\omega^2 x$

Acceleration is maximum when $x=A$

$g=-\omega^2 A$

or $A=\frac{9.8}{\pi^2}$

Maximum velocity $=A \omega$

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

$=\frac{9.8}{\pi} \,m / s$

$=3.119 \,m / s =3.12 \,m / s$

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