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A body of mass 5 kg moving with a velocity 10 m/s collides with another body of mass 20 kg at rest and comes to rest. The velocity of the second body after collision is
- a)2.5 m/s
- b)5 m/s
- c)7.5 m/s
- d)10 m/s
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A body of mass 5 kg moving with a velocity 10 m/s collides with anoth...
m1 = 5 kg, m2 = 20 kg, u1 = 10 m/s, u2 = 0, v1 = 0, v2 = ?
From the law of conservation of momentum:
m1u1 + m2u2 = m1v1 + m2nv2
(5 × 10) + (20 × 0) = (5 × 0) + (20 × v2)
50 = 20v2
v2 = 2.5 m/s
Most Upvoted Answer
A body of mass 5 kg moving with a velocity 10 m/s collides with anoth...
Given:
Mass of the first body (m1) = 5 kg
Velocity of the first body (u1) = 10 m/s
Mass of the second body (m2) = 20 kg
Velocity of the second body (u2) = 0 m/s (at rest)
To find:
Velocity of the second body after collision (v2)
Explanation:
According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Mathematically, this can be represented as:
Initial momentum = Final momentum
Step 1: Calculate the initial momentum:
The initial momentum of the first body (m1) can be calculated using the formula:
Initial momentum of m1 (p1) = mass of m1 (m1) × velocity of m1 (u1)
= 5 kg × 10 m/s
= 50 kg·m/s
Since the second body (m2) is at rest, its initial momentum (p2) is zero.
Therefore, the total initial momentum (p_initial) is the sum of the individual momenta:
p_initial = p1 + p2
= 50 kg·m/s + 0 kg·m/s
= 50 kg·m/s
Step 2: Calculate the final momentum:
After the collision, the first body (m1) comes to rest. Therefore, its final momentum (p1_final) is zero.
The final momentum of the second body (m2) can be calculated using the formula:
Final momentum of m2 (p2_final) = mass of m2 (m2) × velocity of m2 (v2)
Since the first body comes to rest, its final momentum (p1_final) is zero. Therefore, the total final momentum (p_final) is the sum of the individual momenta:
p_final = p1_final + p2_final
= 0 kg·m/s + m2 × v2
According to the law of conservation of momentum, the total initial momentum is equal to the total final momentum:
p_initial = p_final
50 kg·m/s = 0 kg·m/s + 20 kg × v2
v2 = (50 kg·m/s) / (20 kg)
v2 = 2.5 m/s
Therefore, the velocity of the second body after the collision is 2.5 m/s (option A).
Mass of the first body (m1) = 5 kg
Velocity of the first body (u1) = 10 m/s
Mass of the second body (m2) = 20 kg
Velocity of the second body (u2) = 0 m/s (at rest)
To find:
Velocity of the second body after collision (v2)
Explanation:
According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Mathematically, this can be represented as:
Initial momentum = Final momentum
Step 1: Calculate the initial momentum:
The initial momentum of the first body (m1) can be calculated using the formula:
Initial momentum of m1 (p1) = mass of m1 (m1) × velocity of m1 (u1)
= 5 kg × 10 m/s
= 50 kg·m/s
Since the second body (m2) is at rest, its initial momentum (p2) is zero.
Therefore, the total initial momentum (p_initial) is the sum of the individual momenta:
p_initial = p1 + p2
= 50 kg·m/s + 0 kg·m/s
= 50 kg·m/s
Step 2: Calculate the final momentum:
After the collision, the first body (m1) comes to rest. Therefore, its final momentum (p1_final) is zero.
The final momentum of the second body (m2) can be calculated using the formula:
Final momentum of m2 (p2_final) = mass of m2 (m2) × velocity of m2 (v2)
Since the first body comes to rest, its final momentum (p1_final) is zero. Therefore, the total final momentum (p_final) is the sum of the individual momenta:
p_final = p1_final + p2_final
= 0 kg·m/s + m2 × v2
According to the law of conservation of momentum, the total initial momentum is equal to the total final momentum:
p_initial = p_final
50 kg·m/s = 0 kg·m/s + 20 kg × v2
v2 = (50 kg·m/s) / (20 kg)
v2 = 2.5 m/s
Therefore, the velocity of the second body after the collision is 2.5 m/s (option A).
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A body of mass 5 kg moving with a velocity 10 m/s collides with another body of mass 20 kg at rest and comes to rest. The velocity of the second body after collision isa)2.5 m/sb)5 m/sc)7.5 m/sd)10 m/sCorrect answer is option 'A'. Can you explain this answer?
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