Respuesta :
Answer:
Explanation:
Tension in the rope will be due to pseudo -force ( centrifugal force )
Centrifugal force = m rω² where m is mass being rotated and r being distance from the axis and ω is angular velocity. Naturally it will be dependent on r,  distance from the axis.
For terminal mass m attached at the end , the value of this force
F = m  ω² L
For other parts . we shall have to integrate the  values along the length because the value of m x r varies along the length.
Calculate the value of tension for  a small fraction of length dr at distance r along the length .
Mass of the fraction dr = m/L X dr
Tension due to the fraction
dT = m/L  dr X ω² r
Integrating both sides and taking limit from Lto r
T =[tex]\frac{m}{L} \int\limits^L_r {r} \, dr[/tex]
= [tex]\frac{m}{2L}\times(L^2-r^2)[/tex]
Total tension
= F +T
= [tex]\frac{m}{2L}\times(L^2-r^2)[/tex] + m  ω² L
= [tex]\frac{m\omega^2}{2L} ( 3L^2-r^2)[/tex]
