Question

A particle is moving in a circular path of radius a under the action of an attractive potential U = -k/2r². Its total energy is -

Answer 1

Answer: option (2)

Since it is performing circular motion

Comments

for circular orbits Twice the kinetic energy plus the potential energy equals zero (2K + U = 0).But in this case it does not hold.why?

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The virial theorem tells us that for a bound system where the potential energy V is given by an equation:

V(r)∝r^−n
The average kinetic energy T and average potential energy U are related by:

2T=−nU
From the above question, we get n=2
Now putting the value of n in 2T=-nU we get
2T=-2U
Hence, it satisfies the relation.

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When force is calculated as -k/r^3 ,why is the minus sign not included in successive calculations?

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The negative sign means attractive force

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From where you learn this concept

Answer 2

Correct option(2) Zero

Explanation:

It is given that the particle is moving in circular path of radius a under the action of attractive potential, which is given by

Total energy = Kinetic energy + Potential energy

Thus, the total energy is zero.