A coin placed on a rotating table just slips when it is placed at a distance of 1 cm from the center. If the angular velocity of the table is halved, it will just slip when placed at a distance of ----- from the centre:
6 cm
2 cm
4 cm
1 cm
The Correct Option is C
Solution and Explanation
The frictional force is responsible for causing the coin to slip. This force is given by \( f_r = m \cdot \omega^2 r \), where \( \omega \) is the angular velocity and \( r \) is the distance from the center. Given that the angular velocity is halved, we use the equation \( \omega^2 \cdot r^2 = \text{constant} \). When the angular velocity is halved, the distance \( r \) from the center at which the coin slips will be: \[ r_2 = 4 \, \text{cm} \] Thus, when the angular velocity is halved, the coin will slip at a distance of 4 cm from the center.
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Concepts Used:
Laws of Motion
The laws of motion, which are the keystone of classical mechanics, are three statements that defined the relationships between the forces acting on a body and its motion. They were first disclosed by English physicist and mathematician Isaac Newton.
Newton’s First Law of Motion
Newton’s 1st law states that a body at rest or uniform motion will continue to be at rest or uniform motion until and unless a net external force acts on it.
Newton’s Second Law of Motion
Newton's 2nd law of motion deals with the relation between force and acceleration. According to the second law of motion, the acceleration of an object as built by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
Newton’s Third Law of Motion
Newton's 3rd law of motion states when a body applies a force on another body that there is an equal and opposite reaction for every action.