Two blocks and each of mass , are connected by a massless spring of natural length and spring constant . The blocks are initially resting on a smooth horizontal floor with the spring at its natural length, as shown in Fig. A third identical block , also of mass , moves on the floor with a speed along the line joining and and collides elastically with Then

a) |
The kinetic energy of the system, at maximum compression of the spring, is zero |

b) |
The kinetic energy of the system, at maximum compression of the spring, is |

c) |
The maximum compression of the spring is |

d) |
The maximum compression of the spring is |

Two blocks and each of mass , are connected by a massless spring of natural length and spring constant . The blocks are initially resting on a smooth horizontal floor with the spring at its natural length, as shown in Fig. A third identical block , also of mass , moves on the floor with a speed along the line joining and and collides elastically with Then

a) |
The kinetic energy of the system, at maximum compression of the spring, is zero |

b) |
The kinetic energy of the system, at maximum compression of the spring, is |

c) |
The maximum compression of the spring is |

d) |
The maximum compression of the spring is |

1 Answer

127 votes

**(b,d)**

In situation (i), mass is moving towards right with velocity . and are at rest. In situation (ii), which is just after the collision of with , stops and acquires a velocity When starts moving towards right, the spring suffers a compression due to which also starts moving towards right. The compression of the spring continues till there is a relative velocity between and . Once this relative velocity becomes zero, both and move with the same velocity and the spring is in a state of maximum compression

Applying momentum conservation in situations (ii) and (iii),

Therefore, KE of the system in situation (iii) is

Applying energy conservation, we get

Solve to get

127 votes

127