MEDIUM
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Figure shows a block P of mass m resting on a horizontal smooth floor at a distance l from a rigid wall. Block is pushed toward right by a distant 312 and released. When block passes from its mean position another block of mass m1 is placed on it which sticks to it due to friction so that the combined block just collides with the left wall.

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Important Questions on Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics).

HARD
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 a1,a2 and a3 as shown in figure. The system is released from rest with the spring in its unstretched state. The maximum extension of the spring is x0. Which of the following option(s) is/are correct?
[ g is the acceleration due to gravity. Neglect friction]

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HARD
A block with mass M is connected by a massless spring with stiffness constant k to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude A about an equilibrium position x 0 . Consider two cases : (i) when the block is at x0 and (ii) when the block is at x=x0+A. In both the cases, a particle with mass m<M is softly placed on the block after which they stick to each other. Which of the following statement(s) is(are) true about the motion after the mass m is placed on the mass M?