Question

A particle describes a horizontal circle on the smooth surface of an inverted cone. The height of the plane of the circle above the vertex is $9.8cm$. Find the speed of the particle.

• A. $0.98m/s^{-1}$
• B. $1.96m/s^{-1}$
• C. $0.49m/s^{-1}$
• D. $3.92m/s^{-1}$

Answer 1

The correct option is A $0.98m/s^{-1}$

From geometry of figure-

$R\sin \theta =mg-------------1$

$R\cos \theta =\frac{m{v}^2}{r}---------------2$

On dividing equation 1 by 2-

$\tan \theta =\frac{gr}{v^2}$

$\frac{r}{h}=\frac{gr}{v^2}$

$v=\sqrt{gh}$

$v=\sqrt{9.8\times 9.8\times {10}^{-2}}$

$v=0.98m/s$