A 6 kg box is travelling on ice at a speed of 9 m/s when a 12 kg packet is gently placed on it. The velocity will now be
From Principal of conservation of momentum
m 1 v 1 = (m 1 + m 2 ) v
6 Ć 9 = ( 6 + 12) Ć v ā v = 3 m/s
A ball, moving with a speed v towards north, collides with an identical ball, moving with a speed v towards east. After collision the two balls stick together and move towards north-east. The speed of the combination is
Taking both the balls as one system
mv i + mv j= 2mĆ v
so, v= v/2 i + v/2Ā j
so, |v|= v/ā2
A bomb of mass M at rest explodes into three pieces, two of which of mass M/4 each, are thrown off in perpendicular directions with speeds of 3 m/s and 4 m/s. The third piece is thrown off with a speed
As the bomb was initially at rest and no external force acts on it total momentum of the bomb should remain constant.
so, (m/4) 3 i +(m/4) 4 j + (m/2) v1 = 0
v1 = 3/2 i + 4/2 j
|V1|= 2.5 m/s
Assertion: If kinetic energy of a system of particles is zero, then linear momentum of system must be zero.
Reason: If linear momentum of a system of particles is zero, then kinetic energy of system must be zero.
If the kinetic energy of a system is zero, the speed of each particle must be zero, meaning the total linear momentum is also zero. If the total linear momentum is zero, particles can still be moving in opposite directions, resulting in a non-zero kinetic energy. Thus, the Assertion is true but the Reason is false.