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Two bodies of masses m and 4 m are moving with equal kinetic energy. The ratio of velocities with which they are traveling is :
- a)3:4
- b)1:2
- c)4:5
- d)2:1
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Two bodies of masses m and 4 m are moving with equal kinetic energy. T...
since kinetic energies are equal
KE1 = KE2
mv12/2 = 4mv22/2
v1/v2 = √4/1 = 2:1
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Two bodies of masses m and 4 m are moving with equal kinetic energy. T...
Explanation:
Given:
Mass of one body = m
Mass of the other body = 4m
Kinetic energy of both bodies is equal.
Formula:
The formula for kinetic energy is given by:
K.E. = 1/2 * m * v^2
Step 1:
Let the velocity of the first body be v1 and the velocity of the second body be v2.
Step 2:
According to the given condition, the kinetic energy of both bodies is equal:
1/2 * m * v1^2 = 1/2 * (4m) * v2^2
Step 3:
Simplifying the equation, we get:
m * v1^2 = 4m * v2^2
Step 4:
Canceling out the mass term, we have:
v1^2 = 4v2^2
Step 5:
Taking the square root of both sides, we get:
v1 = 2v2
Step 6:
Therefore, the ratio of the velocities is given by:
v1:v2 = 2:1
Conclusion:
The ratio of velocities with which the bodies are traveling is 2:1, which corresponds to option D.
Given:
Mass of one body = m
Mass of the other body = 4m
Kinetic energy of both bodies is equal.
Formula:
The formula for kinetic energy is given by:
K.E. = 1/2 * m * v^2
Step 1:
Let the velocity of the first body be v1 and the velocity of the second body be v2.
Step 2:
According to the given condition, the kinetic energy of both bodies is equal:
1/2 * m * v1^2 = 1/2 * (4m) * v2^2
Step 3:
Simplifying the equation, we get:
m * v1^2 = 4m * v2^2
Step 4:
Canceling out the mass term, we have:
v1^2 = 4v2^2
Step 5:
Taking the square root of both sides, we get:
v1 = 2v2
Step 6:
Therefore, the ratio of the velocities is given by:
v1:v2 = 2:1
Conclusion:
The ratio of velocities with which the bodies are traveling is 2:1, which corresponds to option D.
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Two bodies of masses m and 4 m are moving with equal kinetic energy. The ratio of velocities with which they are traveling is :a)3:4b)1:2c)4:5d)2:1Correct answer is option 'D'. Can you explain this answer?
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