A particle of mass m moving with constant velocity v strikes another p...
Concept:
- Momentum: momentum is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction.
- The unit of momentum (P) is kg m/s.
- Dimension: [MLT-1]
- Law of conservation of Momentum: A conservation law stating that the total linear momentum of a closed system remains constant through time, regardless of other possible changes within the system.
- P1 = P2
- m1 v1 = m2 v2
- Where, P1 = initial momentum of system, P2 = final momentum of system, m1 = mass of first object, v1 = velocity of first object, m2 = mass of second object and v2 = velocity of second object.
Calculation:
Given: m1 = m kg, m2 = m kg, u1 = v m/s, u2 = -v m/s
Let the common velocity of the combined body be V m/s
Mass of combined body M = m + m = 2m
Applying conservation of momentum:
m1 v1 + m2 v2 = M V
mv + (-mv) = 2mV
0 = 2mV
V = 0 m/s
Hence the correct answer will be zero (0) m/s.
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A particle of mass m moving with constant velocity v strikes another p...
Explanation:
When the body of mass m moving with a constant velocity v hits another body of the same mass at rest, the collision is called a perfectly inelastic collision. In a perfectly inelastic collision, the two objects stick together after the collision.
Formula:
In a perfectly inelastic collision, the velocity of the compound body after the collision can be calculated using the following formula:
v' = (m1v1 + m2v2) / (m1 + m2)
Where,
m1 = mass of the first object
v1 = velocity of the first object before collision
m2 = mass of the second object
v2 = velocity of the second object before collision
v' = velocity of the compound body after collision
Calculation:
In this case, both the bodies have the same mass (m) and the first body is moving with a constant velocity v, while the second body is at rest (v2 = 0).
Using the above formula, the velocity of the compound body after collision can be calculated as:
v' = (m1v1 + m2v2) / (m1 + m2)
v' = (mv + 0) / (m + m)
v' = mv / 2m
v' = v / 2
Therefore, the velocity of the compound body after the collision is v/2, which is not one of the given options. However, we know that in a perfectly inelastic collision, the two objects stick together after the collision. Hence, the correct answer is option 'A', which is zero. After the collision, the two bodies are at rest, and their combined velocity is zero.
A particle of mass m moving with constant velocity v strikes another p...
The second body is at rest so m2u2=0
m1v1+m2v2=(m1+m2)V.
V=m1v1/m1+m2
V=mv/2m
V=v/2
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