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Kinetic energy of particles of mass 10 g and 40 g is same, the ratio of their linear momentum is
To find the ratio of the linear momentum of two particles with the same kinetic energy, we can use the formulas for kinetic energy and momentum. Step 1: Write the formula for kinetic energy The kinetic energy (K.E.) is given by: K.E. = (1/2) m v² Where: - m = mass - v = velocity Step 2: Set the kineRead more
To find the ratio of the linear momentum of two particles with the same kinetic energy, we can use the formulas for kinetic energy and momentum.
Step 1: Write the formula for kinetic energy
The kinetic energy (K.E.) is given by:
K.E. = (1/2) m v²
Where:
– m = mass
– v = velocity
Step 2: Set the kinetic energies equal
Let:
– m₁ = 10 g = 0.01 kg
– m₂ = 40 g = 0.04 kg
Since their kinetic energies are the same:
(1/2) m₁ v₁² = (1/2) m₂ v₂²
Cancelling (1/2) from both sides gives:
m₁ v₁² = m₂ v₂²
Step 3: Express velocity in terms of momentum
The momentum (p) is given by:
p = mv
From the above equation:
0.01 v₁² = 0.04 v₂²
Rearranging gives us:
v₁²/v₂² = 0.04/0.01
v₁²/v₂² = 4
Step 4: Find the ratio of velocities
Taking the square root of both sides:
v₁/v₂ = 2
Step 5: Calculate the ratio of momenta
Now, using the definition of momentum:
p₁ = m₁ v₁
p₂ = m₂ v₂
The ratio of their momenta is:
p₁/p₂ = (m₁ v₁) / (m₂ v₂)
p₁/p₂ = (0.01 v₁) / (0.04 v₂)
Substituting the ratio of velocities:
p₁/p₂ = (0.01 * 2v₂) / (0.04 v₂)
p₁/p₂ = (0.02 / 0.04)
p₁/p₂ = 1/2
Final Answer:
The ratio of their linear momentum is 1/2.
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