Question

A body mass 10kg is raised from a certain depth. By the time it is raised by 10m, If its velocity is 2m/s, work done during this time is:
A. 980J
B. 20J
C. 960J
D. 1000J

Answer 1

In this question we will first learn the basics of work and total energy. Further we will use the expression between work done, kinetic energy and potential energy to find the total work done. This will give us the required result.

Formula used:
$W = mgh + \dfrac{1}{2}m{v^2}$

Complete step by step solution:
As we know that the S.I unit of work is joule is represented J. Joule is defined as the work done by a force of one Newton causing a displacement of one meter.
Also, the energy is defined as the ability to do work. Energy can be found in many things and can take different forms, like-kinetic energy is the energy of motion, and potential energy is energy due to an object's position or structure.
So, here we can say that the total work of a system is given by the sum of kinetic energy and potential energy.
$W = mgh + \dfrac{1}{2}m{v^2}$
Now, when we substitute the given values in the above equation, we get:
\eqalign{& W = 10 \times 9.8 \times 10 + \dfrac{1}{2} \times 10 \times 2 \times 2 \cr}
\eqalign{& \Rightarrow W = 980 + 20 \cr}
\eqalign{& \therefore W = 1000J \cr}
Therefore, we get the required result and the correct option is D) i.e., the work done by the body of mass 10kg and having velocity 2m/s, is given by the above result W.
So, the correct answer is “Option D”.

Additional Information: Work can be defined as the measure of energy transfer that occurs when an object is moved over a distance by an external force at least part of which is applied in the direction of the displacement. Further, force experienced by a particle or an object can be defined as the product of mass m and the acceleration a. The S.I. the unit of force is Newton and it is represented as N. The mass of an object is defined as both a property of a physical body and also a measure of its resistance to acceleration or a change in its state of motion, when a net force is applied.
Also it can be said that an object's mass also tells about the strength of its gravitational attraction to other bodies. The SI unit of mass is kilogram or it can be represented as kg.
Pressure applied on an object is defined as the force exerted on the object per unit area.

Note: Here, we should note down that the unit of work can also be given in kilo-Joule, electron volt. From the basic definition of work we can say that when the displacement is zero, which means there is no work done.