Math, asked by mdashikekhan, 4 months ago

10. If the radial velocity of a particle is proportional to its transverse velocity then the
equation of the path of the particle in polar coordinate is
a) r = Aeke, A= arbitrary constant, k=constant of proportionality
b)1= Ae-ke, A= arbitrary constant, k= constant of proportionality
c)r= Aekle, A= arbitrary constant, k=constant of proportionality
d) r= Aek, A= arbitrary constant, k= constant of proportionality​

Answers

Answered by priya5615
2

Answer:

The radial and transverse components which they are moving rapidly with an outward direction.

Where the radial velocity is an object for the path from a fixed point through a straight line.

And the transverse velocity which will refers to an object to a path with an angle θ to the origin path from a fixed point.

radical velocities ∝ transverse velocities

dr/dt ∝ r dθ/dt

dr/dt ∝ λr dθ/dt

Where λ is constant

dr/r = λ dθ

By integrating we get

log r = λθ + log a where log a is constant

Where

log r - log a = λθ

log r/a = λθ

r/a = e^{λθ}

r = ae^{λθ}

Hence it is an equiangular spiral.

Step-by-step explanation:

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