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A 10 kg ball moving with velocity 2 m/s collides with a 20 kg mass initially at rest. If both of them coalesce, the final velocity of combined mass is
To determine the final velocity of the combined mass after the collision, we can use the principle of conservation of momentum. Given: - Mass of ball 1 (m₁) = 10 kg - Velocity of ball 1 (u₁) = 2 m/s - Mass of ball 2 (m₂) = 20 kg - Velocity of ball 2 (u₂) = 0 m/s (initially at rest) Step 1: CalculateRead more
To determine the final velocity of the combined mass after the collision, we can use the principle of conservation of momentum.
Given:
– Mass of ball 1 (m₁) = 10 kg
– Velocity of ball 1 (u₁) = 2 m/s
– Mass of ball 2 (m₂) = 20 kg
– Velocity of ball 2 (u₂) = 0 m/s (initially at rest)
Step 1: Calculate initial momentum
Initial momentum (p_initial) = m₁ * u₁ + m₂ * u₂
p_initial = (10 kg * 2 m/s) + (20 kg * 0 m/s)
p_initial = 20 kg·m/s
Step 2: Compute the final velocity after collision
Let v be the final velocity of the combined mass (m₁ + m₂).
After the collision, the total mass is:
m_total = m₁ + m₂ = 10 kg + 20 kg = 30 kg
According to the conservation of momentum:
p_initial = p_final
20 kg·m/s = (m₁ + m₂) * v
20 kg·m/s = 30 kg * v
Step 3: Solve for v
v = 20 kg·m/s / 30 kg
v = 2/3 m/s
Final Answer:
The final velocity of the combined mass is 2/3 m/s.
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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
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 kgRead more
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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Name the phenomenon which shows the quantum nature of electromagnetic radiation.
The phenomenon that demonstrates the quantum nature of electromagnetic radiation is the photoelectric effect, where light ejects electrons from a material, showing light's particle-like behavior as discrete photons. For more visit here: https://www.tiwariacademy.com/ncert-solutions/class-12/physics/Read more
The phenomenon that demonstrates the quantum nature of electromagnetic radiation is the photoelectric effect, where light ejects electrons from a material, showing light’s particle-like behavior as discrete photons.
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A ball moving with velocity 2 m/s collides head on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in m/s) after collision will be
To solve for the velocities of the balls after collision, we apply the principles of conservation of momentum and the coefficient of restitution. Data given are as follows: - Mass of ball 1 is m₁ = m Velocity of ball 1 is u₁ = 2 m/s Mass of ball 2 is m₂ = 2m (it is double in mass compared to ball 1)Read more
To solve for the velocities of the balls after collision, we apply the principles of conservation of momentum and the coefficient of restitution.
Data given are as follows:
– Mass of ball 1 is m₁ = m
Velocity of ball 1 is u₁ = 2 m/s
Mass of ball 2 is m₂ = 2m (it is double in mass compared to ball 1)
Velocity of ball 2 is u₂ = 0 m/s (ball is at rest)
Coefficient of restitution is e = 0.5
Step 1: Apply the principle of conservation of momentum
The total momentum before the collision is equal to the total momentum after the collision:
m₁ * u₁ + m₂ * u₂ = m₁ * v₁ + m₂ * v₂
Substitute the given values:
m * 2 + 2m * 0 = m * v₁ + 2m * v₂
2m = m * v₁ + 2m * v₂
Divide both sides by m:
2 = v₁ + 2v₂ (Equation 1)
Step 2: Utilization of the coefficient of restitution
Coefficient of restitution is defined by the following equation:
e = (relative speed after collision) / (relative speed before collision)
In this case, it can be derived as
e = (v₂ – v₁) / (u₁ – u₂)
Using the values:
0.5 = (v₂ – v₁) / (2 – 0)
0.5 = (v₂ – v₁) / 2
Multiply both sides by 2
1 = v₂ – v₁ Equation 2
Step 3: Solution of equations
We have two equations
1. v₁ + 2v₂ = 2
2. v₂ – v₁ = 1
From the last equation we may write
v₂ = v₁ + 1
This must be put in the first:
v₁ + 2v₁ + 2 = 2
3v₁ + 2 = 2
3v₁ = 0
v₁ = 0
Inserting the latter into the last of our initial equations:
v₂ = 0 + 1
v₂ = 1
Final velocities after collision:
Velocity of ball 1 (v₁) = 0 m/s
Velocity of ball 2 (v₂) = 1 m/s
Final Answer:
The final velocities after the collision will be 0 m/s, 1 m/s.
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Define the term ‘stopping potential’ in relation to photoelectric effect.
In the photoelectric effect, stopping potential is the minimum negative potential applied to the collector plate that completely stops the most energetic photoelectrons from reaching it, thereby reducing the photocurrent to zero. It represents the maximum kinetic energy of photoelectrons. For more vRead more
In the photoelectric effect, stopping potential is the minimum negative potential applied to the collector plate that completely stops the most energetic photoelectrons from reaching it, thereby reducing the photocurrent to zero. It represents the maximum kinetic energy of photoelectrons.
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