Question

The ball rolls down without slipping (which is at rest at $a$) along $ab$ having friction. It rolls to a maximum height $h_c$ where $bc$ has no friction. $K_a,K_{b}and{K}_c$ are kinetic energies at $a,b$ and $c$.
Which of the following is correct ?

• A. $K_a=K_c,h_a=h_c$
• B. $K_b>K_c,h_a=h_c$
• C. $K_b>K_c,h_a<h_c$
• D. $K_b>K_c,h_a>h_c$

Answer 1

The correct option is D $K_b>K_c,h_a>h_c$

Since the ball rolls without slipping no loss of energy into heat.
initial ball has only P.E.
at $b$ it has K.E. and rot. E.
at $c$ it has P.E. and R.E.( frictionless bc so ball will continue rotating )
so $k_b>k_c$
and ,$h_a>h_c$