Question

A $5kg$ collar is attached to a spring of spring constant $500Nm^{- 1}$ . It slides without friction over a horizontal rod. The collar is displaced from its equilibrium position by $10cm$ and released. The maximum speed is

• A. $1ms^{- 1}$
• B. $5ms^{- 1}$
• C. $10ms^{- 1}$
• D. $20ms^{- 1}$

Answer 1

Answer: (A)

The velocity of the collar executing SHM is given by $v\left(\right.t\left.\right)=-A\omega sin\left(\right.\omega t+\phi\left.\right)$
The maximum speed is given by $v_{m}=A\omega $
Given, $A=10cm=0.1m$
$\omega =\sqrt{\frac{k}{m}}$
$v_{m}=0.1\times \sqrt{\frac{500}{5}}$
$v_{m}=1ms^{- 1}$
it occurs at $x=0$