Three balls and
of masses 2 kg, 4 kg and 8 kg, respectively, move along the same straight line and in the same direction, with velocities 4 m/s, 1 m/s and 3/4 m/s. If
collides with
and subsequently
collides with
, find the velocity of ball
and ball
after collision, taking the coefficient of restitution as unity
a) |
|
b) |
|
c) |
|
d) |
|
Three balls and
of masses 2 kg, 4 kg and 8 kg, respectively, move along the same straight line and in the same direction, with velocities 4 m/s, 1 m/s and 3/4 m/s. If
collides with
and subsequently
collides with
, find the velocity of ball
and ball
after collision, taking the coefficient of restitution as unity
a) |
|
b) |
|
c) |
|
d) |
|
(d)
First consider the collision of balls and
Let the velocities of these two balls after their collision be
and
Momentum after impact = Momentum before impact
(i)
Relative velocity after impact relative velocity before impact
(ii)
Subtracting Eq. (ii) from Eq. (i). we get
m/s
Substituting in Eq. (ii), we get
Hence, after the collision ball is brought to rest, while ball
will move with a velocity of 3 m/s. Now consider the collision of balls
and
. Let the velocities of these balls after collision be
and
respectively
Total momentum after impact = Total momentum before impact
(iii)
Relative velocity after impact = relative velocity before impact
(iv)
Subtracting Eq.(iv) from Eq.(iii), we get
m/s
The system in fig. is released from rest from the position shown. After blocks have moved distance collar
is removed and block
and
continue to move. The speed of
just before it strikes the ground is
a) |
|
b) |
|
c) |
|
d) |
|
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