Question

What is the nature of the graph between K.E. and P.E. of a particle performing a linear S.H.M?
a) A straight line passing through the origin
b) A straight line parallel to the Ek axis
c) straight line having intercepts on the Ep and Ek, axes
d) A straight line parallel to Ep axis​

Answer 1

The nature of the graph between K.E. and P.E. of a particle performing a linear S.H.M is

c) Straight line having intercepts on the Ep and Ek axes

• Kinetic energy and potential energy has values which change with time or at different instants or at different positions of object path. The sum of the kinetic energy and the potential energy of a certain particle or object remains constant.
• The sum being constant, let the kinetic energy of a particle be K and the potential energy of a particle be P, then K + P is constant.
• This equation of the sum of kinetic energy and potential energy of a particle can be re-written as $\frac{K}{a}+\frac{P}{b}=1$ where a and b are arbitrary constants. This is the standard equation of a straight line having intercepts on both the standard axes.

Therefore, The nature of the graph between K.E. and P.E. of a particle performing a linear S.H.M is a straight line having intercepts on the Ep and Ek axes.

Learn more about graphs

https://brainly.in/textbook-solutions/q-fig-11-cf-4-represents-graph-kinetic

Learn more about KE and PE

https://brainly.in/question/13172346?msp_srt_exp=5

Answer 2

Answer:

The nature of the graph between K.E. and P.E. of a particle performing a linear S.H.M is -

c) straight line having intercepts on the Ep and Ek, axes

Explanation:

• Kinetic energy - It is the energy possessed by a body due to its motion. It occurs only in one form, for doing work it doesn't have to be transformed into another form.
• Potential energy - It is the energy possessed by a body on account of its specific state or position. It occurs in various forms like gravitational potential energy and electrical potential energy and work is not done when it is transformed into kinetic energy.
• Kinetic energy and potential energy have values ​​that change over different time and positions along the object's path. The sum of the kinetic energy and the potential energy of a given particle or object remains constant.
• Since the sum is constant, let 'K' be the kinetic energy of a particle and 'P' the potential energy of a particle, then 'K + P' is constant.
• This equation for the sum of the kinetic energy and the potential energy of a particle can be rewritten as -  $\frac{K}{a} + \frac{P}{b} = 1$
• where a and b are arbitrary constants.
• This is the standard equation of a line that has intersections on both  standard axes.

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