Question

A $10\text{kg}$ metal block is attached to a spring of spring constant $1000{\text{Nm}}^{-1}$. A block is displaced from equilibrium position by $10\text{cm}$ and released. The maximum acceleration of the block is

• A. $10{\text{ms}}^{-2}$
• B. $100{\text{ms}}^{-2}$
• C. $200{\text{ms}}^{-2}$
• D. $0.1{\text{ms}}^{-2}$

Answer 1

The correct option is A $10{\text{ms}}^{-2}$

We know that in SHM, the restoring force is proportional to displacement
i.e., $F=-m{\omega }^{2}y...\left(i\right)$
$F=-ky...\left(ii\right)$
where, $k=$ force constant of the spring
Given, $m=10\text{kg},A=10\text{cm}=0.1\text{m},k=1000{\text{Nm}}^{-1}$
Comparing the both equations, we get
${\omega }^2=\frac{k}{m}\Rightarrow \omega =\sqrt{\frac{k}{m}}=\sqrt{\frac{1000}{10}}\Rightarrow 10{\text{rads}}^{-1}$
and acceleration in SHM.
$a_{max}=-{\omega }^2.y=-{10}^2\times \left(0.1\right)=-10{\text{ms}}^{-2}$
Hence magnitude of maximum acceleration is $\simeq 10{\text{ms}}^{-2}$