Question

A uniform rod of length l is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is T(x) at a distance x from the axis, then which of the following graphs depicts it most closely?

Answer 1

The graph which depicts the relation between tension and  x is option (d)

given

Length of rod= l

constant angular speed =ω

distance is x from the axis

the Tension is moving the rod in circle

consider a small amount of mass dm by considering whole mass of rod =M

now to calculate tension in complete rod we need to integrate

∫dt =∫(lim 0 to x)(-m/l.dx)x.ω²

=T(x)=-m/l . x²/2.ω²

we have taken negative sign as T and x are in opposite direction

as only x² is variable and rest are constants

y=-kx²

now the graph of x²is like option (d)