Think about the force that causes a planet to orbit the Sun and the direction of this force. How does a puck swung by a string on the table relate to a planet orbiting the
Sun? What forces are acting on the puck and what forces are acting on the planet

Forces on Puck  Swung

Centrifugal Force (Outwards from  puck swung  )

Tension( Towards the center)

Forces on the Planet

Centrifugal Force (Outwards from  Planets  )

Gravitational Force ( Inwards towards Sun )

Let us suppose that the

The  puck swung is connected with a center at a distance of radius  r

so it is revolving around the point  just like planets revolve around the Sun.

The Centrifugal  Force and Gravitational Force  causes the planetary motion around the sun.

The Centrifugal force is an outward force  and is observed  from the accelerated frame of reference , In our case Planet and  puck swung are    the accelerated frame of references.

The Gravitational Force between the Sun and the planets  (directed towards Sun) is balanced by Centrifugal Force.

Let us consider that the string of  puck swung has negligible mass

So the Tension which is directed towards the center will provide the  force to counterbalance the centrifugal  force acting on puck swung.

So Tension will act towards the center in case of puck swung and centrifugal force will act outwards.

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1) For the swung puck tied to the string that has a mass m₁ and having another mass m₂ attached to the string that passes through a hole in the table, such that m₂ > m₁

The swung puck rotating on the table is kept in the circular motion on the table by the centripetal force acting towards the center of its rotation along the string, which is given by the amount the weight of m₂ exceeds m₁, in the same way a planet moving around the Sun is kept in its orbit by the gravitational attraction between the planet and the Sun.

2) i) The forces acting on the puck are;

a) The centripetal force in the string, acting inward, towards the center of rotation provided by the weight of m₂

b) The centrifugal force of the puck, acting outward, tending to continue its motion in a straight line

ii) The forces acting on the planet are;

a) The force of gravitational attraction between the planet and the Sun, acting towards the Sun, such that, the planet revolves around the Sun

b) The centrifugal force of the planet, acting outward, tending to move in a linear or straight path

Explanation:

increase masses, decrease separation