In the adjoining figure, block A is of mass (m) and block B is of mass2 m. The spring has force constant k. All the surfaces are smooth and the system is released form rest with spring unstretched.
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Options

A. The maximum extension of the spring is `(4mg)/k`.
B. The speed of A when extension in spring is `(2mg)/k` is `2g sqrt((2m)/(3k))`.
C. The acceleration of block B when the extension in the spring is maximum, is `2/3g`
D. Tension in the thread for extension of `(2mg)/(k)` in spring is `mg`

Answer

A

Explanation

(a) Decrease in potential energy of `B=` increase in spring potential
`:. 2mg x_(m)=1/2kx_(m)^(2)`
`:. x_(m)(4mg)/k`
(b) `E_(i) =E_(f)`
`0=1/2(m+2m) v^(2) + 1/2 xxk xx((2mg)/k)^(2)`
`-(2mg)((2mg)/k)`
`:. v=2gsqrt((m)/(3k))`
(c) `a=(kx_(m)-2mg)/(2m) ("upwards")`
`=(k(4mg/k)-2mg)/(2m)=g`
(d)`T-2mg =ma`....(i)
`2mg-T =2mg`......(ii)
Solving these two equations, we get
`a=0` and `T =2mg`
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