Question

The kinetic energy acquired by a mass m in travelling distance d, starting from rest, under the action of a constant force is directly proportional to

• A. m
• B. m$^0$
• C. $\sqrt m$
• D. 1$\sqrt m$

Answer 1

The Correct Option is B

 To solve this question, we need to understand the concept of kinetic energy and how it relates to force and motion.

According to work-energy theorem, the work done by a force on an object is equal to the change in its kinetic energy. If a constant force \(F\) acts on a mass \(m\), starting from rest and moving it over a distance \(d\), the work done \(W\) is given by:

\(W = F \cdot d\)

This work done is converted into kinetic energy \((KE)\) of the mass, so:

\(KE = \frac{1}{2}mv^2\)

Equating the work done to the kinetic energy acquired, we have:

\(F \cdot d = \frac{1}{2}mv^2\) ⇒ \(\frac{1}{2}mv^2 = F \cdot d\)

From Newton's Second Law, we know that \(F = ma\), where \(a\) is the acceleration. Substituting \(F\) into the equation gives:

\(mad = \frac{1}{2}mv^2\)

Assuming a is constant, simplify by dividing through by \(m\):

\(ad = \frac{1}{2}v^2\)

Using the kinematic equation \(v^2 = 2ad\) (since the object starts from rest), we find:

\(2ad = v^2\)

Thus, the distance \(d\) and the acceleration \(a\) actually result from \(v^2 = 2ad\).

Consequently, the kinetic energy \(KE\) is given as:

\(KE = \frac{1}{2}mv^2 = mad = F \cdot d\)

Notice that mass \(m\) merely cancels out on both sides of the equation showing that kinetic energy is independent of mass in this equal proportion. Therefore the kinetic energy acquired is proportional to \(m^0\), which is 1. Thus, it is independent of the mass \(m\).

Hence, the correct answer is:

m\(^0\)