Question

The dimensions of impulse are equal to that of

• A. pressure
• B. linear momentum
• C. force
• D. angular momentum

Answer 1

The Correct Option is B

To determine which physical quantity has the same dimensions as impulse, we need to analyze their dimensional formulas.

Concept Explanation

• Impulse: Impulse is defined as the change in momentum of an object when a force is applied over a period of time. Mathematically, impulse (J) is given by: J = F \cdot \Delta t, where F is the force applied and \Delta t is the time interval.
• Using the dimensional formula, force (F) is [M L T^{-2}] and time (\Delta t) is [T]. Therefore, the dimensional formula for impulse is: [M L T^{-2}] \cdot [T] = [M L T^{-1}].
• Linear Momentum: Linear momentum (p) of an object is given by the product of its mass and velocity, i.e., p = m \cdot v. Thus, its dimensional formula is: [M] \cdot [L T^{-1}] = [M L T^{-1}].

Comparison with Other Options

• Pressure: The dimensional formula for pressure is [M L^{-1} T^{-2}]. This is different from impulse.
• Force: The dimensional formula for force is [M L T^{-2}]. This is different from impulse.
• Angular Momentum: The dimensional formula for angular momentum is [M L^2 T^{-1}]. This is also different from impulse.

Conclusion

Among the given options, the dimensional formula for linear momentum matches that of impulse, which is [M L T^{-1}]. Therefore, the correct answer is linear momentum.