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Q.

Two blocks P & Q of mass m each are attached to two identical springs of spring constant k. Springs are in natural length for the position of blocks shown in figure. Now P is shifted to left by A/2 and Q towards right by A. Both blocks are released simultaneously and collision between them is perfectly inelastic

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a

Time period of oscillation of combined mass is 2πmk

b

Amplitude of oscillation of combined mass is A/4

c

Energy of oscillation of combined mass is 116KA2

d

Time period of oscillation of combined mass is πmk

answer is A.

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Detailed Solution

A) T=2π2m2k=2πmkB) At the time of collision vP=kmA2 and vQ=-kmA Conservation of Momentum, mvP+mvQ=2mvcommon∴Vcommon=-km.A22 =-km.A4 -ve sign means direction is towards left∴Amp=A4 C) E=12kA42+12kA42 =kA216

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