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The amount of work done in stretching a spring from a stretched length of $10 \mathrm{cm}$ to a stretched length of $20 \mathrm{cm}$ is-
(A) Equal to the work done in stretching it from $20 \mathrm{cm}$ to $30 \mathrm{cm}$
(B)Less than the work done in stretching it from $20 \mathrm{cm}$ to $30 \mathrm{cm}$.
(C) More than the work done in stretching it from $20 \mathrm{cm}$ to $30 \mathrm{cm}$.
(D) Equal to the work done in stretching it from 0 to $10 \mathrm{cm}$.

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Last updated date: 17th Apr 2024
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Answer
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Hint: We know that work can be either positive or negative: if the force has a component in the same direction as the displacement of the object, the force is doing positive work. If the force has a component in the direction opposite to the displacement, the force does negative work. One joule is defined as the amount of work done when a force of one newton is exerted through a distance of one meter. In the English system of units, where force is measured in pounds, work is measured in a unit called the foot-pound. When a force acts (pushes or pulls) on an object, it changes the object's speed or direction (in other words, makes it accelerate). The bigger the force, the more the object accelerates. When a force acts on an object, there's an equal force (called a reaction) acting in the opposite direction.

Complete step by step answer
We know that the work-energy principle states that an increase in the kinetic energy of a rigid body is caused by an equal amount of positive work done on the body by the resultant force acting on that body. Conversely, a decrease in kinetic energy is caused by an equal amount of negative work done by the resultant force.
Work done in stretching a spring to $x$ length is $\mathrm{W}=\dfrac{1}{2} \mathrm{kx}^{2}$
$\therefore$ Work one in stretching from $\mathrm{x}_{1}$ to $\mathrm{x}_{2}$ is proportional to $W\propto x_{2}^{2}-x_{1}^{2}$
hence $\dfrac{\mathrm{W}_{20,30}}{\mathrm{W}_{10,20}}=\dfrac{500}{300}$
So, 10 to 20 takes less work when compared to 20 to 30.

Hence the correct answer is option B.

Note: We know that there is a significant difference between work and energy. Work is the transferring of an amount of energy with the help of a force covering a particular distance through a direction. Energy is also referred to as the force which works at a certain distance. An isobaric expansion of a gas requires heat transfer to keep the pressure constant. An isochoric process is one in which the volume is held constant, meaning that the work done by the system will be zero. Work is done whenever a force or a component of a force results in a displacement. No component of the force is acting in the direction of motion when the book is moved horizontally with a constant velocity. The force and the displacement are independent. No work is done by the hand on the book.