A puck of mass `m = 50.0 g` is attached to a taut cord passing through a small hole in a frictionless, horizontal surface (Fig.) The puck is initially orbiting with speed `v_i = 1.50 m//s` in a circle of radius `r_i = 0.30 m`. The cord is then slowly pulled from below, decreasing the radius of the circle to `r = 0.10 m`. The puck's speed at the smaller radius is.
.

Options

A. `2.25 m//s`
B. `5.50 m//s`
C. `4.50 m//s`
D. `6.0 m//s`

Answer

C

Explanation

( c) The puck's linear momentum is always changing. Its mechanical energy changes as work is done on it. Bot its angular momemtum stays constant because although an external force (the tension of the rope) acts on the puck, no external torques act. Therefore, `L` = constant, and at any time, `mvr = mv_i r_i`
Giving us `overline(v =) =(v_i r_i)/( r) = ((1.50 m//s)(0.300 m))/(0.100 m) =450 overline (m//)s`.