Bob P is released from the position of rest at the moment shown. If it collides elastically with an identical bob Q hanging freely then velocity of Q, just after collision is (g = 10 m/s2).
- 1 m/s
- 4 m/s
- 2 m/s
- 8 m/s
The Correct Option is C
Solution and Explanation
The velocity of object \( P \) just before the collision is given as:
\[ v_P = \sqrt{2gl} \]
Substituting the given values:
\[ v_P = 2 \, \text{m/s} \]
Since the collision is elastic and the masses of \( P \) and \( Q \) are equal, the following conditions apply:
- Just after the collision, the velocity of \( P \) becomes \( 0 \).
- The velocity of \( Q \) becomes equal to the initial velocity of \( P \), which is \( 2 \, \text{m/s} \).
Reasoning
- In an elastic collision, momentum and kinetic energy are conserved.
- When two bodies of equal mass collide elastically:
- The moving body transfers all its velocity to the stationary body.
- The initial moving body comes to rest.
Conclusion
After the collision:
\[ v_P = 0 \quad \text{and} \quad v_Q = 2 \, \text{m/s} \]
Therefore, the correct answer is:
\[ \boxed{2 \, \text{m/s}} \]
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Concepts Used:
Kinematics
Kinematics is a branch of physics that deals with the study of motion, without considering the forces that cause the motion. It is concerned with the position, velocity, and acceleration of objects, as well as the time it takes for them to move from one point to another.
In kinematics, the motion of an object is represented using mathematical equations and graphs. The most common quantities used in kinematics are displacement, velocity, acceleration, and time.
Displacement refers to the change in position of an object, and it is represented by the symbol Δx. Velocity is the rate at which an object's position changes over time, and it is represented by the symbol v. Acceleration is the rate at which an object's velocity changes over time, and it is represented by the symbol a.
Also Read: Kinematics Formula
By analyzing the relationships between these quantities, kinematics can be used to predict the motion of objects in different situations. For example, kinematics can be used to calculate the maximum height reached by a projectile, the distance traveled by a car during a given time, or the time it takes for a rollercoaster to complete a loop.
Kinematics is used in many areas of physics, including mechanics, astrophysics, and robotics. It is also used in engineering, where it is used to design and optimize the motion of machines and vehicles.