Work Energy Theorem

Step 1: Understanding the Question:
The problem asks for the ratio of the masses of two bodies, given the ratio of their kinetic energies and the fact that they have equal linear momentum.
Step 2: Key Formula or Approach:
1. Kinetic Energy ( ):
2. Linear Momentum ( ):
These two are related by: . This form is convenient when momentum is constant.
Step 3: Detailed Explanation:
Let the two bodies be 1 and 2.
Given:
- Ratio of kinetic energies:
- Equal linear momentum:
Using the relation :
For body 1:
For body 2:
Now, take the ratio of their kinetic energies:
We are given .
So, .
The question asks for the ratio of their masses ( ):

Step 4: Final Answer:
The ratio of their masses is 1:3.

Step 1: Understanding the Question:
The problem asks for the change in kinetic energy of a body after a constant force acts on it for a specific time, starting from rest on a frictionless surface.
Step 2: Key Formula or Approach:
1. Newton's second law: .
2. Kinematics (from rest): .
3. Kinetic Energy: .
4. Work-Energy Theorem: .
Alternatively, we can find the final velocity and then the final kinetic energy.
Step 3: Detailed Explanation:
Given values:
- Force,
- Mass,
- Initial velocity, (at rest)
- Time,
First, calculate the acceleration ( ):
Next, calculate the final velocity ( ) after 10 s:
Now, calculate the change in kinetic energy ( ):
Since it starts from rest, initial kinetic energy .
Final kinetic energy

Step 4: Final Answer:
The change in kinetic energy of the body is 250 J.