Kinetic energy of particles of mass 10 g and 40 g is same, the ratio of their linear momentum is
Linear momentum is the measure of an object’s motion in a straight line. It is calculated as the product of an object’s mass and velocity. Represented as p = m * v, linear momentum is a vector quantity and is conserved in isolated systems during collisions or interactions.
Chapter 5 of Class 11 Physics focuses on work energy and power. It explains the calculation of work done by a force energy transformations the law of conservation of energy and forms of energy like kinetic and potential. Power is introduced as the rate of doing work.
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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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