Question

A spring with spring constant K when compressed by 1cn, the potential energy stored is U, if it is further compressed by 3cm, then charge in its potential energy is
A) 3U
B) 9U
C) 8U
D) 15U

Answer 1

Hint: Heat is a form of energy. Energy is the capacity to do the work and energy exists in different forms. From the law of conservation energy can neither be created nor be distorted but it can be transformed to another form. SI unit of energy is joule (J) and energy is a scalar quantity which has only magnitude.

Complete step-by-step answer:
Potential energy is the energy possessed by an object due to its relative stationary position in space, stress, or electric charge. Potential energy is the inherent energy of the body relative to its static position to the other objects. Potential energy is one of the two main types of energy, while the other is kinetic energy.
The potential energy is stored if a spring is compressed by a Force of F,
 Potential energy turns into kinetic energy when spring is realized
 The potential energy which is stored in a spring is given by:
$U=\dfrac{1}{2}K{{(x)}^{2}}$
Where $x$ = net compression
From the data net compression ($x$ ) =1cm
Substituting these values in the above equation
$\begin{align}
  & U=\dfrac{1}{2}K{{(1)}^{2}} \\
 & U=\dfrac{K}{2} \\
\end{align}$
When the net compression is further compressed by 3cm,
Then net compression ${{x}^{1}}=3+1=4cm$
So the total potential energy is given by:
${{U}^{1}}=\dfrac{1}{2}K{{({{x}^{1}})}^{2}}=\dfrac{1}{2}K{{(4)}^{2}}=8K$
On comparing the potential energy in a spring and total potential energy
 $\begin{align}
  & \dfrac{{{U}^{1}}}{U}=16 \\
 & {{U}^{1}}=16U \\
\end{align}$

So, the correct answer is “Option A”.

Note: Student’s kinetic energy is always associated with motion and conservation of energy principle is also called as the first law of thermodynamics. There are different types of energy and that is potential or stored, kinetic, thermal, electrical, chemical and nuclear energy. The dimensional formula of energy is $M{{L}^{2}}{{T}^{-2}}$.