Question

A particle of mass $m$ moves along the internal smooth surface of a vertical cylinder of radius $r$. Find the force with which the particle acts on the cylinder wall if at $t=0$, its velocity is $v_0$ and it makes an angle $\alpha$ with the horizontal.

• A. $\frac{m{v_0}^2}{R}$
• B. $\frac{m{v_0}^2}{R}\cos \alpha$
• C. $\frac{m{v_0}^2\sin \alpha }{R}$
• D. $\frac{m{v_0}^2{\cos }^2\alpha }{R}$

Answer 1

Answer: (D)

$\frac{m{v_0}^2{\cos }^2\alpha }{R}$

Here the force is the centrifugal force. i.e
$F=\frac{m{v}^2}{r}=\frac{m(v_0\cos \alpha {)}^2}{R}=\frac{m{v}_0^2{\cos }^2\alpha }{R}$