Question

The kinetic energy acquired by a body of mass \( M \) in travelling a certain distance \( d \), starting from rest, under the action of constant force is

• A. inversely proportional to \( \sqrt{M} \)
• B. directly proportional to \( M \)
• C. independent of \( M \)
• D. directly proportional to \( \sqrt{M} \)

Hint:

When a constant force is applied, the kinetic energy acquired by the body is independent of its mass and only depends on the force and distance.

Answer 1

The Correct Option is C

Step 1: Understanding the work-energy principle.
The work done by a constant force on a body is given by: \[ W = F \times d \] where \( F \) is the force applied and \( d \) is the distance travelled. The work done is equal to the change in kinetic energy, and since the body starts from rest, the kinetic energy acquired by the body is: \[ K.E. = F \times d \] Step 2: Force and mass relationship.
Since force is constant, the kinetic energy acquired by the body is independent of its mass \( M \), and only depends on the applied force and the distance travelled.
Step 3: Conclusion.
Thus, the kinetic energy acquired is independent of mass \( M \), which is option (C).