A 10 kg metal block is attached to a spring constant `1000 Nm^(-1)`. A block is displaced from equilibrium position by 10 cm and released. The maximum acceleration of the block is

Options

A. `10 ms^(-2)`
B. `100 ms^(-2)`
C. `200 ms^(-2)`
D. `0.1 ms^(-2)`

Answer

A

Explanation

We know that, spring does SHM.
So, the restoring force is proportional to displacement
i.e. `F = -m omega^(2)y" "...(i)`
`F = - ky" "...(ii)`
where, k = force constant of the spring
`m = 10 kg, k = 1000 Nm^(-1)`
`A = 10 cm = 0.1 m`
On comparing both equations, we get
`omega^(2)=(k)/(m)`
`rArr" "omega=sqrt((k)/(m))=sqrt((1000)/(10))=10 rad//s`
and acceleration in SHM
`a_(max) =- omega^(2)."y where," omega^(2)` is constant
`=-10^(2)xx(0.1)=-10m//s^(2)=10 ms^(-2)`