Problem 413 - JEE Physics

Question

The force acting on a body whose linear momentum changes by \(20 \mathrm{kgms}^{-1}\) in \(10 \mathrm{sec}\) is (A) \(2 \mathrm{~N}\) (B) \(20 \mathrm{~N}\) (C) \(200 \mathrm{~N}\) (D) \(0.2 \mathrm{~N}\)

Step-by-Step Solution

Answer

Using the formula \(F = \frac{\Delta p}{\Delta t}\), we can find the force acting on the body when its linear momentum changes by \(20\,\mathrm{kgms}^{-1}\) in \(10\,\mathrm{sec}\). Plugging in the given values, we get \(F = \frac{20\,\mathrm{kgms}^{-1}}{10\,\mathrm{sec}} = 2 \,\mathrm{N}\). Comparing our result to the given options, the correct answer is option (A) \(2 \mathrm{~N}\).

Step 1: Write down the formula for force

From Newton's second law of motion, we have the formula for force: \[F = \frac{\Delta p}{\Delta t}\]

Step 2: Plug in the given values

Now, we will substitute the given values into the formula: \(\Delta p = 20\,\mathrm{kgms}^{-1}\) and \(\Delta t = 10\,\mathrm{sec}\) \[F = \frac{20\,\mathrm{kgms}^{-1}}{10\,\mathrm{sec}}\]

Step 3: Calculate the force

We will now perform the division operation to find the force: \[F = 2 \,\mathrm{N}\]

Step 4: Choose the correct option

Comparing our result to the given options, we find that the force acting on the body is : (A) \(2 \mathrm{~N}\) So, the correct answer is option (A).

Key Concepts

Force Calculation

Understanding force calculation is crucial when dealing with dynamics in physics. Newton's Second Law of Motion is the fundamental principle used to calculate force. According to this law, the force acting on an object is equal to the rate of change of its momentum. This can be mathematically expressed as \[ F = \frac{\Delta p}{\Delta t} \]where \( F \) is the force, \( \Delta p \) is the change in momentum, and \( \Delta t \) is the change in time. By substituting known values into this formula, one can determine the exact force exerted on an object under certain conditions. It is important to measure the momentum change and time accurately for precise force calculations. Simplifying these calculations will enable a better understanding of the forces involved.

Linear Momentum

Linear momentum is a key concept in physics that helps understand how objects move. It is defined as the product of an object's mass and its velocity, represented by the formula \[ p = m \cdot v \]where \( p \) is the momentum, \( m \) is the mass of the object, and \( v \) is its velocity. Momentum is a vector quantity, meaning it has both a magnitude and a direction. Conservation of momentum is a crucial concept stating that in an isolated system, the total momentum remains constant, if no external forces act on it. When dealing with problems involving momentum change, such as the calculation of force, knowing how momentum interacts and transfers between objects is essential.

Physics Problem Solving

Solving physics problems often involves understanding the core principles and applying them to real-world scenarios. Here's a simple guide to approach problem-solving:

• Read the problem carefully and identify what is given and what needs to be found.
• Recall relevant concepts, like Newton's Laws, and find applicable formulas.
• Substitute given values into the formulas.
• Perform the necessary calculations to arrive at the solution.
• Double-check the calculations and the logic of your answer.

Staying organized and systematic while working through problems helps in avoiding mistakes, ensuring that the physical principles are applied correctly and efficiently.

Dynamics

Dynamics is a branch of physics that studies the forces and torques and their effect on motion. It distinguishes itself from kinematics, as kinematics only describes how objects move, while dynamics explains why objects move. Understanding dynamics involves:

• Identifying forces acting on an object, such as gravity, friction, and tension.
• Applying Newton's Laws to determine how these forces affect motion.
• Analyzing scenarios involving acceleration and deceleration.
• Understanding the impact of external forces and torques on an object's state of motion.

The study of dynamics is essential for solving a wide array of engineering and physics problems, providing insights into how and why objects behave the way they do under various forces.