Problem 414 - JEE Physics

Question

An impulsive force of \(100 \mathrm{~N}\) acts on a body for \(1 \mathrm{sec}\) What is the change in its linear momentum ? (A) \(10 \mathrm{~N}-\mathrm{S}\) (B) \(100 \mathrm{~N}-\mathrm{S}\) (C) \(1000 \mathrm{~N}-\mathrm{S}\) (D) \(1 \mathrm{~N}-\mathrm{S}\)

Step-by-Step Solution

Answer

The change in linear momentum is \(100 \mathrm{~N}-\mathrm{S}\).

Step 1: Recall the impulse-momentum theorem formula

The formula for the impulse-momentum theorem is given as: Impulse = Change in Momentum Impulse = Force × Time Change in Momentum = Force × Time

Step 2: Plug in the given values and calculate the change in momentum

From the problem, the force is 100 N and the time is 1 sec. Plug these values into the formula: Change in Momentum = 100 N × 1 s Change in Momentum = 100 N·s

Step 3: Compare our result with the options

Our calculation gave us a change in momentum of 100 N·s. Compare this result to the options given. The correct answer is: (B) \(100 \mathrm{~N}-\mathrm{S}\)

Key Concepts

Linear Momentum

Linear momentum is a fundamental concept in physics that describes the motion of an object. It is defined as the product of an object's mass and velocity. Mathematically, we express linear momentum, \( p \), as:

\[p = m \times v\]where \( m \) is the mass of the object and \( v \) is its velocity.

Linear momentum has both magnitude and direction, making it a vector quantity. This means that if an object's velocity changes direction, its momentum will as well. Understanding momentum is crucial because it helps predict how objects behave in motion and interactions.

• It conserves in the absence of external forces, meaning if no net external force acts, the total momentum remains constant.
• It implies interactions between objects that can cause transfers of momentum from one object to another.

Impulse Calculation

Impulse is a concept closely tied to momentum. It's essentially a measure of how much force is applied over a given time period. The mathematical definition of impulse, \( J \), is:

\[J = F \times \Delta t\]where \( F \) is the force applied and \( \Delta t \) is the time duration over which the force is acting.

The impulse experienced by an object is equal to the change in its momentum, as given by the impulse-momentum theorem:
\[J = \Delta p\]This theorem states that the impulse applied to an object results in a change in its momentum. In calculations:

• Identify the force \( F \) and the time \( \Delta t \).
• Multiply these values for impulse \( J \).

For the given problem, applying a force of 100 N over 1 second gives an impulse of 100 N·s, which equals the change in momentum.

Change in Momentum

A change in momentum occurs when a force is applied to an object over a period of time. According to the impulse-momentum theorem, the change in momentum \( \Delta p \) can be calculated using:

\[\Delta p = F \times \Delta t\]In the exercise problem, applying a force of 100 N for 1 second results in a change in momentum of 100 N·s. This means that the momentum of the object has increased or decreased depending on the direction of the force applied.

Understanding how momentum changes is key to analyzing collisions and other interactions.

• If an impulse causes an increase in momentum, it accelerates the object.
• A decrease would decelerate or change the direction of the object.

So, changes in momentum help explain the outcomes of many physical interactions observed in everyday life.