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A ball of mass 5 kg moving at 3 m/s collides with another ball of mass 3 kg moving at 5 m/s in the same direction. If the balls move together after the collision in the same direction, find their common velocity.
- a)5 m/s
- b)3.75 m/s
- c)6.25 m/s
- d)7.5 m/s
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A ball of mass 5 kg moving at 3 m/s collides with another ball of mass...
Given:
Mass of ball 1 (m1) = 5 kg
Velocity of ball 1 (u1) = 3 m/s
Mass of ball 2 (m2) = 3 kg
Velocity of ball 2 (u2) = 5 m/s
After the collision, the balls move together in the same direction.
To find: Common velocity of the balls after the collision.
Solution:
1. First, we need to find the momentum of each ball before the collision using the formula:
Momentum (p) = Mass (m) x Velocity (u)
Momentum of ball 1 before the collision (p1) = m1u1 = 5 kg x 3 m/s = 15 kg m/s
Momentum of ball 2 before the collision (p2) = m2u2 = 3 kg x 5 m/s = 15 kg m/s
2. Next, we need to find the total momentum of the system before the collision (p):
Total momentum before the collision (p) = p1 + p2 = 15 kg m/s + 15 kg m/s = 30 kg m/s
3. During the collision, the balls stick together and move with a common velocity (v). Using the law of conservation of momentum, we can equate the total momentum before the collision (p) to the total momentum after the collision (p'):
Total momentum after the collision (p') = (m1 + m2) x v
4. Equating the two expressions for total momentum, we get:
p = p'
30 kg m/s = (5 kg + 3 kg) x v
5. Solving for v, we get:
v = 30 kg m/s ÷ 8 kg = 3.75 m/s
Therefore, the common velocity of the balls after the collision is 3.75 m/s.
Answer: Option B (3.75 m/s)
Mass of ball 1 (m1) = 5 kg
Velocity of ball 1 (u1) = 3 m/s
Mass of ball 2 (m2) = 3 kg
Velocity of ball 2 (u2) = 5 m/s
After the collision, the balls move together in the same direction.
To find: Common velocity of the balls after the collision.
Solution:
1. First, we need to find the momentum of each ball before the collision using the formula:
Momentum (p) = Mass (m) x Velocity (u)
Momentum of ball 1 before the collision (p1) = m1u1 = 5 kg x 3 m/s = 15 kg m/s
Momentum of ball 2 before the collision (p2) = m2u2 = 3 kg x 5 m/s = 15 kg m/s
2. Next, we need to find the total momentum of the system before the collision (p):
Total momentum before the collision (p) = p1 + p2 = 15 kg m/s + 15 kg m/s = 30 kg m/s
3. During the collision, the balls stick together and move with a common velocity (v). Using the law of conservation of momentum, we can equate the total momentum before the collision (p) to the total momentum after the collision (p'):
Total momentum after the collision (p') = (m1 + m2) x v
4. Equating the two expressions for total momentum, we get:
p = p'
30 kg m/s = (5 kg + 3 kg) x v
5. Solving for v, we get:
v = 30 kg m/s ÷ 8 kg = 3.75 m/s
Therefore, the common velocity of the balls after the collision is 3.75 m/s.
Answer: Option B (3.75 m/s)
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Community Answer
A ball of mass 5 kg moving at 3 m/s collides with another ball of mass...
Let 'v' be the common velocity. . Then Using law of conservation of momentum... we have: m1u1+m2u2=(m1+m2)v... =》(5×3)+(3×5)=(5+3)v.. =》30=8v.. =》v=30/8=3.75 m/s..
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A ball of mass 5 kg moving at 3 m/s collides with another ball of mass 3 kg moving at 5 m/s in the same direction. If the balls move together after the collision in the same direction, find their common velocity.a)5 m/sb)3.75 m/sc)6.25 m/sd)7.5 m/sCorrect answer is option 'B'. Can you explain this answer?
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