CBSE Class 11-science Answered

" the radius of the depth well in a circus is 25m"

We take this to mean the radius of the vertical loop and solve.

Let the minimum speed be v_min, then the kinetic energy is, mv_min²/2.

If we consider the bottom point as reference for potential energy zero, then potential energy at highest point is,

mg(2R) = 2mgR

At the highest point the centripetal force is provided by weight of the performer and bike,

mv²/R = mg

v² = Rg

Hence KE at the highest point is mRg/2 and potential energy 2mgR

So total energy =  mRg/2 + 2mgR = 5mgR/2,

This must be equal to the total energy at bottom, KE + PE = mv_min²/2 + 0

mv_min²/2 = 5mgR/2

v_min = (5gR)

Regards,

Team,

TopperLearning.