All questions of Unit for UPSC CSE Exam

Understanding the Pendulum's Behavior on a Train
When analyzing the behavior of a pendulum on a moving train, it is essential to understand the forces acting on the pendulum and how they relate to the train's motion.
1. Pendulum Orientation
- If the pendulum's string is pointing towards the front of the train, it indicates that the pendulum is experiencing a net force in that direction.
2. Acceleration and Forces
- A pendulum at rest or moving at a constant speed would have its string hanging vertically downwards, indicating no net horizontal forces acting on it.
- When the train accelerates, the pendulum swings backward relative to the train due to inertia. The bob will lag behind the vertical line, creating an angle where the string points toward the front.
3. Conclusion: Moving with Retardation
- If the pendulum’s string points forward, the train must be accelerating backward (decelerating) relative to the pendulum's inertia. Thus, it is indeed moving with retardation.
- The pendulum's swing indicates the relative motion of the train. Hence, with the string directed forward, it confirms the train is decelerating.
Final Insight
- The answer is 'C' - Moving with retardation, as the pendulum's position reveals the train's changing speed. Understanding force and motion principles clarifies this dynamic relationship.

Given data:
Acceleration (a) = 2.6 m/s^2
Force (F) = 90 N

Formula:
The relationship between force, mass, and acceleration is given by Newton's second law of motion:
F = ma
Where:
F = force
m = mass
a = acceleration

Calculations:
Given force (F) = 90 N
Acceleration (a) = 2.6 m/s^2
Using the formula F = ma, we can rearrange it to find the mass (m):
m = F/a
m = 90 N / 2.6 m/s^2
m ≈ 34.6 kg
Therefore, the mass of the body is approximately 34.6 kg. Hence, option 'b' is the correct answer.

Frictional Force Direction
Frictional force always acts opposite to the direction of the applied force. In this case, the force is provided parallel to the surface to move the block of wood. Therefore, the frictional force will act in the opposite direction to this applied force.

Explanation
When a force is applied to move an object along a surface, the frictional force comes into play to resist this motion. The frictional force acts in the opposite direction to the applied force, making it more difficult for the object to move.

Role of Frictional Force
The frictional force helps in maintaining the stability of the object on the surface and prevents it from sliding uncontrollably. It also plays a crucial role in various everyday activities such as walking, driving, and even gripping objects.

Importance of Understanding Frictional Force Direction
Understanding the direction of the frictional force is essential for predicting how an object will move when a force is applied. It helps in determining the amount of force required to overcome friction and move the object smoothly.

Conclusion
In the given scenario, the frictional force will act opposite to the direction of the applied force provided parallel to the surface. This knowledge of the frictional force direction is crucial for effectively moving objects and predicting their behavior on flat surfaces.