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A mass of 20 kg moving with a speed of 10 m/s collides with another stationary mass of 5 kg. As a result of the collision, the two masses stick together. The kinetic energy of the composite mass will be
- a)600 J
- b)800 J
- c)1000 J
- d)1200 J
Correct answer is option 'B'. Can you explain this answer?
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A mass of 20 kg moving with a speed of 10 m/s collides with another st...
Given:
Mass of first object, m1 = 20 kg
Initial velocity of first object, u1 = 10 m/s
Mass of second object, m2 = 5 kg
Initial velocity of second object, u2 = 0 (since it is stationary)
The two objects stick together after collision.
To find:
Kinetic energy of the composite mass after collision.
Solution:
1. Conservation of momentum:
Before the collision, total momentum of the system = m1u1 + m2u2
= 20 × 10 + 5 × 0
= 200 kg m/s
After the collision, the two objects stick together, so the final velocity of the composite mass, v = ?
By conservation of momentum, total momentum of the system after collision = total momentum before collision
m1u1 + m2u2 = (m1 + m2)v
20 × 10 + 5 × 0 = (20 + 5)v
v = 200/25
v = 8 m/s
2. Kinetic energy:
Before the collision, total kinetic energy of the system = 1/2 m1u1^2 + 1/2 m2u2^2
= 1/2 × 20 × 10^2 + 1/2 × 5 × 0^2
= 1000 J
After the collision, the two objects stick together, so the final kinetic energy of the composite mass, K = ?
K = 1/2 (m1 + m2) v^2
= 1/2 (20 + 5) × 8^2
= 800 J
Therefore, the kinetic energy of the composite mass after collision is 800 J.
Answer: Option B.
Mass of first object, m1 = 20 kg
Initial velocity of first object, u1 = 10 m/s
Mass of second object, m2 = 5 kg
Initial velocity of second object, u2 = 0 (since it is stationary)
The two objects stick together after collision.
To find:
Kinetic energy of the composite mass after collision.
Solution:
1. Conservation of momentum:
Before the collision, total momentum of the system = m1u1 + m2u2
= 20 × 10 + 5 × 0
= 200 kg m/s
After the collision, the two objects stick together, so the final velocity of the composite mass, v = ?
By conservation of momentum, total momentum of the system after collision = total momentum before collision
m1u1 + m2u2 = (m1 + m2)v
20 × 10 + 5 × 0 = (20 + 5)v
v = 200/25
v = 8 m/s
2. Kinetic energy:
Before the collision, total kinetic energy of the system = 1/2 m1u1^2 + 1/2 m2u2^2
= 1/2 × 20 × 10^2 + 1/2 × 5 × 0^2
= 1000 J
After the collision, the two objects stick together, so the final kinetic energy of the composite mass, K = ?
K = 1/2 (m1 + m2) v^2
= 1/2 (20 + 5) × 8^2
= 800 J
Therefore, the kinetic energy of the composite mass after collision is 800 J.
Answer: Option B.
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A mass of 20 kg moving with a speed of 10 m/s collides with another stationary mass of 5 kg. As a result of the collision, the two masses stick together. The kinetic energy of the composite mass will bea)600 Jb)800 Jc)1000 Jd)1200 JCorrect answer is option 'B'. Can you explain this answer?
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