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A body of mass 10 kg and velocity 10 m/s collides with a stationary body of mass 5 kg. After collision both bodies stick to each other, velocity of the bodies after collision will be
- a)3/10 m/s
- b)18/3 m/s
- c)9/20 m/s
- d)20/3 m/s
Correct answer is option 'D'. Can you explain this answer?
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A body of mass 10 kg and velocity 10 m/s collides with a stationary bo...
Given data:
Mass of first body (m1) = 10 kg
Velocity of first body (u1) = 10 m/s
Mass of second body (m2) = 5 kg
Velocity of second body (u2) = 0 m/s (since it is stationary)
Let's denote the final velocity of the combined bodies as v.
To solve this problem, we can use the principle of conservation of momentum, which states that the total momentum of an isolated system remains constant before and after a collision.
1. Calculate the initial momentum:
The initial momentum of the system is given by the sum of the individual momenta of the two bodies before the collision.
Initial momentum = m1 * u1 + m2 * u2
= 10 kg * 10 m/s + 5 kg * 0 m/s
= 100 kg.m/s
2. Calculate the final momentum:
The final momentum of the system is given by the sum of the individual momenta of the two bodies after the collision.
Final momentum = (m1 + m2) * v
According to the principle of conservation of momentum,
Initial momentum = Final momentum
m1 * u1 + m2 * u2 = (m1 + m2) * v
Substituting the given values,
10 kg * 10 m/s + 5 kg * 0 m/s = (10 kg + 5 kg) * v
100 kg.m/s = 15 kg * v
3. Calculate the final velocity:
Dividing both sides of the equation by 15 kg, we get
v = 100 kg.m/s / 15 kg
v ≈ 6.67 m/s
Therefore, the velocity of the bodies after the collision is approximately 6.67 m/s.
However, none of the given options match this result. It seems there might be an error in the options provided.
Mass of first body (m1) = 10 kg
Velocity of first body (u1) = 10 m/s
Mass of second body (m2) = 5 kg
Velocity of second body (u2) = 0 m/s (since it is stationary)
Let's denote the final velocity of the combined bodies as v.
To solve this problem, we can use the principle of conservation of momentum, which states that the total momentum of an isolated system remains constant before and after a collision.
1. Calculate the initial momentum:
The initial momentum of the system is given by the sum of the individual momenta of the two bodies before the collision.
Initial momentum = m1 * u1 + m2 * u2
= 10 kg * 10 m/s + 5 kg * 0 m/s
= 100 kg.m/s
2. Calculate the final momentum:
The final momentum of the system is given by the sum of the individual momenta of the two bodies after the collision.
Final momentum = (m1 + m2) * v
According to the principle of conservation of momentum,
Initial momentum = Final momentum
m1 * u1 + m2 * u2 = (m1 + m2) * v
Substituting the given values,
10 kg * 10 m/s + 5 kg * 0 m/s = (10 kg + 5 kg) * v
100 kg.m/s = 15 kg * v
3. Calculate the final velocity:
Dividing both sides of the equation by 15 kg, we get
v = 100 kg.m/s / 15 kg
v ≈ 6.67 m/s
Therefore, the velocity of the bodies after the collision is approximately 6.67 m/s.
However, none of the given options match this result. It seems there might be an error in the options provided.
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A body of mass 10 kg and velocity 10 m/s collides with a stationary body of mass 5 kg. After collision both bodies stick to each other, velocity of the bodies after collision will bea)3/10 m/sb)18/3 m/sc)9/20 m/sd)20/3 m/sCorrect answer is option 'D'. Can you explain this answer?
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