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Two bodies of masses m and 4m. are moving with equal kinetic energies. The ratio of their linear momenta is
Linear momentum is the product of a body’s mass and velocity, representing the quantity of motion. It is a vector quantity, having both magnitude and direction. Momentum is conserved in isolated systems, making it crucial in understanding collisions and dynamics. Examples include a moving car or a rolling ball.
Class 11 Physics Chapter 5 Work, Energy and Power focuses on the concepts of work energy and power. It covers the relationships between these quantities and their applications in mechanics and real-world scenarios, crucial for CBSE EXAM 2024-25.
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For a relation between the linear momenta of the two bodies moving with equal kinetic energies, we use the relation of kinetic energy with momentum.
Step 1: Kinetic energy and momentum relation
The kinetic energy K.E. is related to the momentum p by,
Kinetic energy = p2 / (2m)
Now, rearranging in terms of momentum we get,
p = √(2m × K.E.)
Step 2: Given
For the two bodies
Mass of the first body = m
Mass of the second body = 4m
– Both have the same kinetic energy.
Let the kinetic energy of both bodies be \\( K.E. \\).
Step 3: Calculate the momentum of each body
For the first body:
p₁ = √(2m × K.E.)
For the second body:
p₂ = √(2 × 4m × K.E.) = √(8m × K.E.)
Step 4: Find the ratio of momenta
The ratio of their momenta is:
p₁ : p₂ = √(2m × K.E.) : √(8m × K.E.)
p₁ : p₂ = √2 : √8
p₁ : p₂ = 1 : 2
The ratio of their linear momenta is: 1 : 2
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