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Two particles collide in air ( 2 kg and 4 kg) just before collision they are travelling horizontally at a great height with velocity of C. M at 80 m/ s. what will be the velocity of C. M 6 sec after collision ( g= 10 m/s^2).?
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Two particles collide in air ( 2 kg and 4 kg) just before collision th...
Given:
Mass of first particle (m1) = 2 kg
Mass of second particle (m2) = 4 kg
Velocity of center of mass (Vcm) = 80 m/s
Time after collision (t) = 6 sec
Acceleration due to gravity (g) = 10 m/s^2
Calculating the velocity of center of mass after collision:
Step 1: Calculate the initial momentum of the system before collision.
Initial momentum = (mass of first particle * velocity of first particle) + (mass of second particle * velocity of second particle)
Step 2: Calculate the final momentum of the system after collision.
Final momentum = (mass of first particle * velocity of first particle after collision) + (mass of second particle * velocity of second particle after collision)
Step 3: Apply the principle of conservation of momentum.
According to the principle of conservation of momentum, the initial momentum of the system before collision is equal to the final momentum of the system after collision.
Step 4: Rearrange the equation to solve for the velocity of the center of mass after collision.
Final momentum = (mass of first particle * velocity of first particle after collision) + (mass of second particle * velocity of second particle after collision)
Final momentum = (m1 * V1cm) + (m2 * V2cm)
Step 5: Substitute the given values into the equation.
Final momentum = (2 kg * V1cm) + (4 kg * V2cm)
Step 6: Apply the principle of conservation of momentum.
Initial momentum = Final momentum
(mass of first particle * velocity of center of mass before collision) + (mass of second particle * velocity of center of mass before collision) = (mass of first particle * velocity of first particle after collision) + (mass of second particle * velocity of second particle after collision)
Step 7: Substitute the given values into the equation and solve for the velocity of the center of mass after collision.
(2 kg * 80 m/s) + (4 kg * 80 m/s) = (2 kg * V1cm) + (4 kg * V2cm)
Simplifying the equation:
160 kg m/s + 320 kg m/s = 2 kg * V1cm + 4 kg * V2cm
480 kg m/s = 2 kg * V1cm + 4 kg * V2cm
Step 8: Solve the equation to find the velocity of the center of mass after collision.
V1cm + 2V2cm = 240 m/s
We are given that the time after collision is 6 seconds. Using the equation of motion:
V = U + at
Step 9: Calculate the final velocities of the particles after 6 seconds.
V1cm = 80 m/s + (0 m/s^2 * 6 s)
V1cm = 80 m/s
V2cm = 80 m/s + (10 m/s^2 * 6 s)
V2cm = 140 m/s
Step 10: Substitute the values of V1cm and V2cm into the equation from Step
Mass of first particle (m1) = 2 kg
Mass of second particle (m2) = 4 kg
Velocity of center of mass (Vcm) = 80 m/s
Time after collision (t) = 6 sec
Acceleration due to gravity (g) = 10 m/s^2
Calculating the velocity of center of mass after collision:
Step 1: Calculate the initial momentum of the system before collision.
Initial momentum = (mass of first particle * velocity of first particle) + (mass of second particle * velocity of second particle)
Step 2: Calculate the final momentum of the system after collision.
Final momentum = (mass of first particle * velocity of first particle after collision) + (mass of second particle * velocity of second particle after collision)
Step 3: Apply the principle of conservation of momentum.
According to the principle of conservation of momentum, the initial momentum of the system before collision is equal to the final momentum of the system after collision.
Step 4: Rearrange the equation to solve for the velocity of the center of mass after collision.
Final momentum = (mass of first particle * velocity of first particle after collision) + (mass of second particle * velocity of second particle after collision)
Final momentum = (m1 * V1cm) + (m2 * V2cm)
Step 5: Substitute the given values into the equation.
Final momentum = (2 kg * V1cm) + (4 kg * V2cm)
Step 6: Apply the principle of conservation of momentum.
Initial momentum = Final momentum
(mass of first particle * velocity of center of mass before collision) + (mass of second particle * velocity of center of mass before collision) = (mass of first particle * velocity of first particle after collision) + (mass of second particle * velocity of second particle after collision)
Step 7: Substitute the given values into the equation and solve for the velocity of the center of mass after collision.
(2 kg * 80 m/s) + (4 kg * 80 m/s) = (2 kg * V1cm) + (4 kg * V2cm)
Simplifying the equation:
160 kg m/s + 320 kg m/s = 2 kg * V1cm + 4 kg * V2cm
480 kg m/s = 2 kg * V1cm + 4 kg * V2cm
Step 8: Solve the equation to find the velocity of the center of mass after collision.
V1cm + 2V2cm = 240 m/s
We are given that the time after collision is 6 seconds. Using the equation of motion:
V = U + at
Step 9: Calculate the final velocities of the particles after 6 seconds.
V1cm = 80 m/s + (0 m/s^2 * 6 s)
V1cm = 80 m/s
V2cm = 80 m/s + (10 m/s^2 * 6 s)
V2cm = 140 m/s
Step 10: Substitute the values of V1cm and V2cm into the equation from Step
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Two particles collide in air ( 2 kg and 4 kg) just before collision they are travelling horizontally at a great height with velocity of C. M at 80 m/ s. what will be the velocity of C. M 6 sec after collision ( g= 10 m/s^2).?
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Two particles collide in air ( 2 kg and 4 kg) just before collision they are travelling horizontally at a great height with velocity of C. M at 80 m/ s. what will be the velocity of C. M 6 sec after collision ( g= 10 m/s^2).? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two particles collide in air ( 2 kg and 4 kg) just before collision they are travelling horizontally at a great height with velocity of C. M at 80 m/ s. what will be the velocity of C. M 6 sec after collision ( g= 10 m/s^2).? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two particles collide in air ( 2 kg and 4 kg) just before collision they are travelling horizontally at a great height with velocity of C. M at 80 m/ s. what will be the velocity of C. M 6 sec after collision ( g= 10 m/s^2).?.
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