A 10 kg object at rest explodes into four pieces. Each of the three pieces has a mass of 2.0 kg, and the
pieces travel due south, due east, and due west, respectively, at 3.0 m/s. What is the magnitude of the
velocity of the remaining piece?
(A) 1.0 m/s (B) 1.5 m/s (C) 3.0 m/s (D) 4.5 m/s
Answers
Answered by
4
Given:-
Mass of object = 10kg
Mass of three Pieces = 2kg
Velocity of 3 Piece = 3.0m/s
To Find:-
The magnitude of the Velocity of the remaining Piece.
Formulae used:-
Conservation of Momentum
Now,
→ We know that the total mass if object is 10kg so and mass of 3 Pieces is 2kg so mass of 4th Piece would be (10 - 6) → 4kg.
Therefore,
Initially the Object was at rest.
So,
→ Total Momenta before exploding = Total Momenta after exploding.
→ 0 = m¹v¹ + m²v² + m³v³ + m⁴v⁴
→ 0 = ( m¹ + m² + m³ ) v + m⁴v⁴
→ 0 = ( 2 + 2 + 2)3 + m⁴v⁴
→ 0 = (6)3 + m⁴v⁴
→ 0 = 18 + m⁴v⁴
→ -18 = 4 × v⁴
→ v⁴ = -18/4
→ v⁴ = -4.5m/s
Hence, Option "D" is correct.
Answered by
18
- A 10 kg object at rest explodes into four pieces.
- Each of the three pieces has a mass of 2.0 kg,
- the pieces travel due south, due east, and due west, respectively, at 3.0 m/s.
- What is the magnitude of the velocity of the remaining piece?
.
Total Momenta before exploding
Option d is correct
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