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 x 0 ; and (ii) when the block is at x = x 0 + 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?
, whereas in the second case it remains unchanged
Text Solution
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(a, b, d)
Case-1
Case-2
In case-1
MV 1 = (M + m)V 2
V 2 = 
V 1
A 2 = 
A 1
A 2 = 
A 1
In case-2
A 2 = A 1
T = 2 π 
in both case.
Total energy decreases in first case where as remain same in 2 nd case.
instantaneous speed at x 0 decreases in both case.
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