Question

A small solid ball rolls down along sufficiently rough surface from 1 to 3 as shown in figure. From point-3 onwards it moves under gravity. Match the following two columns

Answer 1

(a) $K_{Total}=mgh$
$\frac{K_R}{K_T}=\frac{2}{5}$
$\therefore K_T=\frac{5}{7}K=\frac{5}{7}mgh$
b) $K_{Total}=mg\frac{h}{2}$
$\frac{K_R}{K_T}=\frac{2}{5}$
$\therefore K_r=\frac{5}{7}\left(mg\frac{h}{2}\right)=\frac{5}{14}mgh$
c) At 3 $\therefore K_R=\frac{2}{7}\left(mg\frac{h}{2}\right)=\frac{1}{7}mgh$
From 3 to 4, $K_R$ will become constant.
d) $K_T=K_{Total}-K_R$
$=mgh-\frac{1}{7}mgh=\frac{6}{7}mgh$