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Blocks A and B shown in the figure are h...

Blocks A and B shown in the figure are having equal masses m. The system is released from rest with the spring unstretched. The string between A and ground is cut, when there is maximum extension in the spring. The acceleration of centre of mass of the two blocks at this instant is

A

g

B

`(g)/(2)`

C

2g

D

zero

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Initially block shown is at rest and the spring is unstretched, when a constant force F begins to act on it neglect friction. Find maximum extension in the spring

Consider the situation shown in figure. Mass of block A is m and that of blcok B is 2m. The force constant of string is k. Friction is absent everywhere. System is released from rest with the spring unstretched. Find (a) The maximum extension of the spring x_(m) (b) The speed of block A when the extension in the springt is x=(x_(m))/(2) (c ) The net acceleration of block B when extension in the spring is x=(x_(m))/(4).

Knowledge Check

  • In the shown diagram mass of A is m and that of B is 2 m. All the surfaces are smooth. System is released from rest with spring unstretched. Then, the maximum extension (x_(m)) in spring will be:

    A
    `(mg)/(k)`
    B
    `(2mg)/(k)`
    C
    `(3 mg)/(k)`
    D
    `(4 mg)/(k)`

  • The system is released from rest with both the springs in unstretched positions. Mass of each block is 1 kg and force constant of each spring is 10 N//m . In the equilibrium position, speed of the block placed horizontally is

    A
    `3.21 m//s`
    B
    `2.21 m//s`
    C
    `1.93 m//s`
    D
    `1.26 m//s`

  • A block of mass 2M is attached to a massless spring with spring-constant k. This block is connected to two other blocks of masses M and 2M using two massless pulleys and strings. The accelerations of the blocks are a_(1)a_(2) and a_(3) as shown in the figure. The system is released from rest with the spring in its unstretched state. The maximum extension of the spring is x_(0) Which of the following option(s) is(are) correct? [g is the acceleration due to gravity. Neglect friction]

    A
    `a_(2)-a_(1)=a_(1)-a_(2)`
    B
    At an extension of `(x_(0))/(4)`of the spring, the magnitude of acceleration of the block connected to the spring is `(3g)/(10)`
    C
    `x_(0)=(4Mg)/(k)`
    D
    When spring achieves an extension of `(x_(0))/(2)` for the first time, the speed of the block connected to the spring is `3g(M)/(5K)`

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