A mass, fastened to the end of a steel wire of unstretched length , is whirled in a vertical circle with an angular velocity of at the bottom of the circle. The cross-sectional area of the wire is . Calculate the elongation of the wire when the mass is at the lowest point of its path.
Step 1: Given Data
Mass of the body
Length of the steel wire
The cross-sectional area of the wire
We know that Young's modulus
Step 2: Calculate the Force
The wire is fastened to a given mass and is rotating with the given angular velocity.
The forces acting on the wire are the weight of the mass and the centrifugal force due to the circular motion with a radius .
Therefore, the total force assuming is given as,
Step 3: Calculate the Elongation
We know that Young's modulus is given by
where , where is the force,
Upon substituting the values we get,
Hence, the elongation of the wire when the mass is at the lowest point of its path is .