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A 1 kg stationary bomb exploded in three parts having mass ratio 1:1:3 . Parts having same mass are moving in perpendicular direction with velocity 30m/s, then the velocity of bigger part will be
- a)10 √2 m/s
- b)10/√2 m/s
- c)15 √s m/s
- d)15/s m/s
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A 1 kg stationary bomb exploded in three parts having mass ratio 1:1:3...
Conservation of momentum
1×0=1 ×30i +1×30j +3v
3v= -(30i +30j)
v = -(10i +10j)
v ( magnitude)= √(10)²+(10)²
=10√2 m/s
1×0=1 ×30i +1×30j +3v
3v= -(30i +30j)
v = -(10i +10j)
v ( magnitude)= √(10)²+(10)²
=10√2 m/s
Most Upvoted Answer
A 1 kg stationary bomb exploded in three parts having mass ratio 1:1:3...
Given data:
- Mass of the bomb (m) = 1 kg
- Mass ratio of the parts = 1:1:3
- Velocity of two parts with equal mass = 30 m/s
Calculating masses of the parts:
- Let the masses of the three parts be m1, m2, and m3.
- Given that the mass ratio is 1:1:3, we can represent the masses as m1 = x, m2 = x, and m3 = 3x.
- Since the total mass of the bomb is 1 kg, we have: x + x + 3x = 1
- Solving the equation, we get x = 1/5 kg.
Calculating velocities of the parts:
- Total momentum before the explosion = 0 (as the bomb is stationary)
- Total momentum after the explosion = m1v1 + m2v2 + m3v3
- Given that m1 = m2 = 1/5 kg and v1 = v2 = 30 m/s, and m3 = 3/5 kg, we have:
0 = (1/5)(30) + (1/5)(30) + (3/5)v3
0 = 6 + (3/5)v3
v3 = -10 m/s
Calculating the velocity of the bigger part:
- The bigger part has a mass of 3/5 kg and velocity of -10 m/s.
- Since velocity is a vector quantity, the negative sign indicates that the bigger part is moving in the opposite direction.
- The magnitude of the velocity of the bigger part = |-10| = 10 m/s
- Therefore, the velocity of the bigger part is 10 m/s.
Hence, the correct answer is option 'A' - 10√2 m/s.
- Mass of the bomb (m) = 1 kg
- Mass ratio of the parts = 1:1:3
- Velocity of two parts with equal mass = 30 m/s
Calculating masses of the parts:
- Let the masses of the three parts be m1, m2, and m3.
- Given that the mass ratio is 1:1:3, we can represent the masses as m1 = x, m2 = x, and m3 = 3x.
- Since the total mass of the bomb is 1 kg, we have: x + x + 3x = 1
- Solving the equation, we get x = 1/5 kg.
Calculating velocities of the parts:
- Total momentum before the explosion = 0 (as the bomb is stationary)
- Total momentum after the explosion = m1v1 + m2v2 + m3v3
- Given that m1 = m2 = 1/5 kg and v1 = v2 = 30 m/s, and m3 = 3/5 kg, we have:
0 = (1/5)(30) + (1/5)(30) + (3/5)v3
0 = 6 + (3/5)v3
v3 = -10 m/s
Calculating the velocity of the bigger part:
- The bigger part has a mass of 3/5 kg and velocity of -10 m/s.
- Since velocity is a vector quantity, the negative sign indicates that the bigger part is moving in the opposite direction.
- The magnitude of the velocity of the bigger part = |-10| = 10 m/s
- Therefore, the velocity of the bigger part is 10 m/s.
Hence, the correct answer is option 'A' - 10√2 m/s.
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A 1 kg stationary bomb exploded in three parts having mass ratio 1:1:3 . Parts having same mass are moving in perpendicular direction with velocity 30m/s, then the velocity of bigger part will bea)10 √2 m/sb)10/√2 m/sc)15 √s m/sd)15/s m/sCorrect answer is option 'A'. Can you explain this answer?
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