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
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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 
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 Thena)
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
Question ID - 100686 | SaraNextGen Top Answer 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 |
|
b) |
The kinetic energy of the |
|
c) |
The maximum compression of the spring is |
|
d) |
The maximum compression of the spring is |
(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
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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