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Q8. A ball of mass 2 kg is moving with a constant velocity of 6 m/s towards east. It hits a stationary ball of mass 4 kg . After the impact the first ball comes to rest; however, the 2nd ball, breaks into two equal parts. Part 1 of the ball goes towards north with a velocity of 2√3 m/s. Findthedirection and velocity of part 2 of the 2nd ball. [Draw Schematic diagram].?
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Q8. A ball of mass 2 kg is moving with a constant velocity of 6 m/s to...
Problem Overview
A 2 kg ball moves east at 6 m/s and collides with a stationary 4 kg ball. After the collision, the first ball stops, and the second ball breaks into two equal parts.
Schematic Diagram
- Ball A (2 kg) → Initial velocity = 6 m/s (East)
- Ball B (4 kg) → Initial velocity = 0 m/s (Stationary)
- After collision:
- Ball A stops
- Ball B splits into two parts (2 kg each)
- Part 1 moves north at 2√3 m/s
Conservation of Momentum
The law of conservation of momentum states that total momentum before the collision equals total momentum after the collision.
Initial Momentum Calculation
- Initial momentum of Ball A:
Momentum_A_initial = mass_A * velocity_A = 2 kg * 6 m/s = 12 kg·m/s (East)
- Initial momentum of Ball B:
Momentum_B_initial = 0 (stationary)
Total initial momentum = 12 kg·m/s (East)
Final Momentum Calculation
After the collision, the first ball comes to rest, and the second ball breaks into two parts:
- Momentum of Part 1 (2 kg) moving north at 2√3 m/s:
Momentum_Part1 = mass * velocity = 2 kg * 2√3 m/s = 4√3 kg·m/s (North)
Let the velocity of Part 2 be v and move at an angle θ. Its momentum can be expressed as:
Momentum_Part2 = 2 kg * v (at angle θ).
Setting Up the Equations
Using momentum conservation in both x (East-West) and y (North-South) directions:
- In the x-direction:
12 = 2v * cos(θ)
- In the y-direction:
0 = 4√3 - 2v * sin(θ)
By solving these equations, we find the direction and velocity of Part 2.
Conclusion
Through conservation of momentum, you can determine the velocity and direction of the second part of the ball after the collision.
A 2 kg ball moves east at 6 m/s and collides with a stationary 4 kg ball. After the collision, the first ball stops, and the second ball breaks into two equal parts.
Schematic Diagram
- Ball A (2 kg) → Initial velocity = 6 m/s (East)
- Ball B (4 kg) → Initial velocity = 0 m/s (Stationary)
- After collision:
- Ball A stops
- Ball B splits into two parts (2 kg each)
- Part 1 moves north at 2√3 m/s
Conservation of Momentum
The law of conservation of momentum states that total momentum before the collision equals total momentum after the collision.
Initial Momentum Calculation
- Initial momentum of Ball A:
Momentum_A_initial = mass_A * velocity_A = 2 kg * 6 m/s = 12 kg·m/s (East)
- Initial momentum of Ball B:
Momentum_B_initial = 0 (stationary)
Total initial momentum = 12 kg·m/s (East)
Final Momentum Calculation
After the collision, the first ball comes to rest, and the second ball breaks into two parts:
- Momentum of Part 1 (2 kg) moving north at 2√3 m/s:
Momentum_Part1 = mass * velocity = 2 kg * 2√3 m/s = 4√3 kg·m/s (North)
Let the velocity of Part 2 be v and move at an angle θ. Its momentum can be expressed as:
Momentum_Part2 = 2 kg * v (at angle θ).
Setting Up the Equations
Using momentum conservation in both x (East-West) and y (North-South) directions:
- In the x-direction:
12 = 2v * cos(θ)
- In the y-direction:
0 = 4√3 - 2v * sin(θ)
By solving these equations, we find the direction and velocity of Part 2.
Conclusion
Through conservation of momentum, you can determine the velocity and direction of the second part of the ball after the collision.
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Q8. A ball of mass 2 kg is moving with a constant velocity of 6 m/s towards east. It hits a stationary ball of mass 4 kg . After the impact the first ball comes to rest; however, the 2nd ball, breaks into two equal parts. Part 1 of the ball goes towards north with a velocity of 2√3 m/s. Findthedirection and velocity of part 2 of the 2nd ball. [Draw Schematic diagram].?
Question Description
Q8. A ball of mass 2 kg is moving with a constant velocity of 6 m/s towards east. It hits a stationary ball of mass 4 kg . After the impact the first ball comes to rest; however, the 2nd ball, breaks into two equal parts. Part 1 of the ball goes towards north with a velocity of 2√3 m/s. Findthedirection and velocity of part 2 of the 2nd ball. [Draw Schematic diagram].? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Q8. A ball of mass 2 kg is moving with a constant velocity of 6 m/s towards east. It hits a stationary ball of mass 4 kg . After the impact the first ball comes to rest; however, the 2nd ball, breaks into two equal parts. Part 1 of the ball goes towards north with a velocity of 2√3 m/s. Findthedirection and velocity of part 2 of the 2nd ball. [Draw Schematic diagram].? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q8. A ball of mass 2 kg is moving with a constant velocity of 6 m/s towards east. It hits a stationary ball of mass 4 kg . After the impact the first ball comes to rest; however, the 2nd ball, breaks into two equal parts. Part 1 of the ball goes towards north with a velocity of 2√3 m/s. Findthedirection and velocity of part 2 of the 2nd ball. [Draw Schematic diagram].?.
Q8. A ball of mass 2 kg is moving with a constant velocity of 6 m/s towards east. It hits a stationary ball of mass 4 kg . After the impact the first ball comes to rest; however, the 2nd ball, breaks into two equal parts. Part 1 of the ball goes towards north with a velocity of 2√3 m/s. Findthedirection and velocity of part 2 of the 2nd ball. [Draw Schematic diagram].? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Q8. A ball of mass 2 kg is moving with a constant velocity of 6 m/s towards east. It hits a stationary ball of mass 4 kg . After the impact the first ball comes to rest; however, the 2nd ball, breaks into two equal parts. Part 1 of the ball goes towards north with a velocity of 2√3 m/s. Findthedirection and velocity of part 2 of the 2nd ball. [Draw Schematic diagram].? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q8. A ball of mass 2 kg is moving with a constant velocity of 6 m/s towards east. It hits a stationary ball of mass 4 kg . After the impact the first ball comes to rest; however, the 2nd ball, breaks into two equal parts. Part 1 of the ball goes towards north with a velocity of 2√3 m/s. Findthedirection and velocity of part 2 of the 2nd ball. [Draw Schematic diagram].?.
Solutions for Q8. A ball of mass 2 kg is moving with a constant velocity of 6 m/s towards east. It hits a stationary ball of mass 4 kg . After the impact the first ball comes to rest; however, the 2nd ball, breaks into two equal parts. Part 1 of the ball goes towards north with a velocity of 2√3 m/s. Findthedirection and velocity of part 2 of the 2nd ball. [Draw Schematic diagram].? in English & in Hindi are available as part of our courses for UPSC.
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