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The given arrangement is released from r...

The given arrangement is released from rest when spring is in natural length. Maximum extension in spring during the motion is `x_(0). a_(1),a_(2)` and `a_(3)` are accelerations of the blocks. Make the correct options

A

`a_(2)-a_(1)=a_(1)-a_(3)`

B

`x_(0)=(4mg)/(3k)`

C

Velocity of 2m connected to spring when elongation is `(x_(0))/(2)` is `v = (x_(0))/(2)sqrt((3k)/(14m))`

D

acceleration `a_(1)` at `(x_(0))/(4)` is `(3k x_(0))/(42m)`

Text Solution

Verified by Experts


`2a_(1)=a_(2)+a_(3)`
`a_(1)-a_(3)=a_(2)-a_(1)`
for other options use m equivalent

`(T)/(g')=(2(2m)(m))/(2m+m)=(4m)/(3)`
`(2T)/(g')=(8m)/(3)`
`m_(eq.)=(4m(2m))/(m+2m)=(8m)/(3)`

`(1)/(2)kx_(0)^(2)=(8mg)/(3)x_(0)`
`x_(0)=(16mg)/(3k)`
`V_((x_(0))/(2))=V_(max)=(x_(0))/(2)w=(x_(0))/(2)sqrt((k)/(2m+(8m)/(3)))=(x_(0))/(2)sqrt((3k)/(14m))`
`a_((x_(0))/(4))=(x_(0))/(4)w^(2)=(x_(0))/(4)(3k)/(14m)=(3kx_(0))/(42m)`
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