Physics

Which of the following statement(s) is(are) true about the motion after the mass $m$ is placed on the mass $M$?

Solution:

In case I,From Conservation of momentum,

$MV_{1}=(M+m)V_{2}$

$M+mMV_{1} =V_{2}$

$M+mk A_{2}=M+mM Mk A_{1}$

$A_{2}=M+mM A_{1}$

In case II,

$A_{2}=A_{1}$

$T=2πkM+m $ in both the cases.

Total energy decreases in first case where as remain same in 2nd case.

Instantaneous speed at $x_{0}$ decreases in both case.

Solution:

The maximum elongation occurs when the velocity of both the particles becomes equal. Since there is no external force acting in the horizontal direction (for the

blocks + spring system), thus the linear momentum is conserved in horizontal direction:

If the final common velocity is $V$

$5×3+2×10=(5+2)VV=5ms_{−1}$

Also applying law of conservation of energy for the system (work done by non-conservative force is zero):

Initial Energy $=$ Final Energy

$21 ×5×3_{2}+21 ×2×10_{2}=21 ×1120x_{2}+21 ×7×5_{2}$

Solving the above equation we get $x=25$ cm

Also it can be observed that the compression and expansion occur alternately.

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