A toy car shaped like a sphere with mass m and radius r is placed on a toy track that includes a vertical loop of radius R. Find the minimum height h from which the toy must start to complete the loop if (A) r<<R, (B) no assumption of r with R, assuming it rolls without slipping and there are no energy losses due to friction or air resistance.

• A. $h_A=2.5R,\ \ h_B=2.7\left(R-r\right)$
• B. $h_A=2.7R,\ \ h_B=2.5(R-r)$
• C. $h_A=3.0R,\ \ h_B=3.0\left(R-r\right)$
• D. $h_A=3.5R,\ \ h_B=3.5\left(R-r\right)$

Answer: (A)