Question

A skier starts at the top of a snowball with negligible speed and skis straight down the side. At what point does he lose contact with the snowball:

• A. $\theta =si{n}^{-1}\frac{2}{3}$
• B. $\theta =co{s}^{-1}\frac{2}{3}$
• C. $\theta =ta{n}^{-1}\frac{2}{3}$
• D. none of the above

Answer 1

Answer: (B)

$\theta =co{s}^{-1}\frac{2}{3}$

Using conservation of energy,
$\frac{m{v}^2}{2}=mgh=mgR(1-cos\theta )$
or $\frac{m{v}^2}{R}=2mg(1-cos\theta )$
Condition of losing contact is N=0,
$\frac{m{v}^2}{R}=mgcos\theta -N$
Putting N=0 in above equation will get,
$\frac{m{v}^2}{R}=mgcos\theta$
or $2mg(1-cos\theta )=mgcos\theta$ or $\theta =co{s}^{-1}\frac{2}{3}$