৪৯তম বিসিএস ⎯ গণিত [৫৫১]

When a particle moves in a straight line so that its acceleration is always directed towards a fixed point on the line and varies directly as the distance from the point, then its motion is called Simple Harmonic Motion.

If a particle of mass m moves in a straight under the action of a force varying as the distance towards a fixed point in the line and the motion is resisted by a force proportional to the velocity, then the motion of the particle is called Damped oscillation.

When a particle moves in a straight line so that its acceleration is always directed towards a fixed point on the line and varies directly as the distance from the point, then its motion is called Simple Harmonic Motion. So the distance be x unit then the equation of Simple Harmonic Motion

The periodic time (পর্যায়কাল) for the Simple Harmonic Motion

মনে করি, পতনশীল একক ভরের  বস্তুটি t সময়ে কেন্দ্র হতে x দূরত্বে অবস্থান করে।

If the time period of simple harmonic motion is T, then angular frequency ( কৌণিক বেগ ) is 2π/T

In a central orbit, the point at which the radius vector is maximum or minimum is called apse point.

According to the Kepler’s laws, the shape of the orbit of a planet is elliptical.

The periodic time of a particle move in an ellipse under a central force is T=2π/√μ  a^(3/2)

A single orbit can have at most two apsidal distance- one maximum and one minimum.

Kepler’s second law says that the line joining  a planet and the Sun sweeps out equal areas in equal intervals of time, meaning the areal velocity remains constant.

According to the Kepler’s third law, the square of the orbital period of a planet is  directly proportional to the cube of the semi-major axis of its orbit.

Kepler’s first law clarifies that the Sun is never at the center of the ellipse but always located at one of its foci, while the other focus remains empty.

সঠিক উত্তর: central orbit.
অপশনে সঠিক উত্তর না থাকায় প্রশ্নটি বাতিল করা হয়েছে। 
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The path described by the particle moving along a plane curve under central force is called central orbit.

The rate of change of velocity of a particle is called acceleration.

For simple harmonic motion (d²x)/(dt²)=-μx is possible when μ>0

If a body moves in a circular path of radius r with velocity v, the formula for central force is F = (mv²)/r

The work done by central force is always Zero.

Central force is a Real force

The equation of motion of a particle in a central force is

কেন্দ্রিক কক্ষপথের উপর অসংখ্য আয়ান্ত বিন্দু থাকতে পারে।