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 :- (g=10 m / s 2)

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 :- (g=10 m / s 2) (A) 1.57 ms -1 (B) 3.14 ms -1 (C) 1 ms -1 (D) 6.42 ms -1

Tardigrade Admin · Accepted Answer

a max =ω2 A=g when N=0 T=2 sec so ω=π ⇒ A=(g/ω2)=(10/π2)=1 m and V max =ω A=3.14 m / s

Q. 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 :- $(g = 10 m / s^{2})$

$1.57 m s^{- 1}$

$3.14 m s^{- 1}$

$1 m s^{- 1}$

$6.42 m s^{- 1}$

$a_{m a x} = ω^{2} A = g$
${$ when $N = 0}$
$T = 2 sec$ so $ω = π$
$\Rightarrow A = \frac{g}{ω ^{2}} = \frac{10}{π ^{2}} = 1 m$
and $V_{m a x} = ω A = 3.14 m / s$

Q. A block is resting on a piston which executes simple harmonic motion with a period 2.0s. The maximum velocity of the piston, at an amplitude just sufficient for the block to separate from the piston is :- (g=10m/s2)

1.57ms−1

3.14ms−1

1ms−1

6.42ms−1