A body of mass 5 kg, moving with velocity 10 m/sec collides with another body of the mass 20 kg at rest and comes to rest. The velocity of the second body due to collision is
A collision occurs when two or more bodies exert forces on each other during their interaction. Collisions can be elastic or inelastic. In elastic collisions, both momentum and kinetic energy are conserved while inelastic collisions conserve momentum but not kinetic energy. Understanding collisions is crucial in mechanics and engineering.
Chapter 5 of Class 11 Physics focuses on Work Energy and Power. It explores the relationship between work and energy along with the various forms of energy such as kinetic and potential energy. The chapter also covers the concept of power efficiency and the work-energy theorem essential for solving problems in the CBSE exam.
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We can apply the principle of conservation of momentum to calculate the velocity of the second body after the collision.
Step 1: Write the momentum before and after collision
Let,
m₁ = Mass of the first body = 5 kg
u₁ = Initial velocity of the first body = 10 m/s
m₂ = Mass of the second body = 20 kg
– Starting velocity of the second body (u₂) = 0 m/s (at rest)
– Final velocity of both bodies after collision (v₁) = 0 m/s (first body comes to rest)
– Final velocity of the second body (v₂) = ?
Applying the principle of conservation of momentum:
Initial momentum = Final momentum
m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂
(5 kg × 10 m/s) + (20 kg × 0 m/s) = (5 kg × 0 m/s) + (20 kg × v₂)
Step 2: Find v₂
50 kg·m/s = 0 + 20 kg × v₂
50 kg·m/s = 20 kg × v₂
Divide both sides by 20 kg
v₂ = 50 kg·m/s / 20 kg
v₂ = 2.5 m/s
Final Answer:
The velocity of the second body due to the collision is 2.5 m/sec.
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