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A 10 kg metal block is attached to a spr...

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

A

`10 ms^(-2)`

B

`100 ms^(-2)`

C

`200 ms^(-2)`

D

`0.1 ms^(-2)`

Text Solution

Verified by Experts

The correct Answer is:
A
(a) We know that in spring SHM , the restoring force is proportional to displacement
i.e., `F=-momega^(2)y" "…(i)`
`F=-ky" "…(ii)`
where ,k =force constant of the spring
m=10 kg `implies` A=10 cm =0.1 m `implies` k`=1000 Nm^(-1)`
Comparing the both equations , we get
`omega^(2)=(k)/(m)impliesomega=sqrt((k)/(m))=sqrt((1000)/(10))implies 10 " rads"^(-1)`
and acceleration in SHM.
`a_("max")=-omega^(2).y=-10^(2)xx(0.1)=-10ms^(-2)underline~ 10 ms^(-2)`
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