Question 182: Work, Energy and Power & Circular Motion

Question

A particle describes a horizontal circle on smooth inner surface of a cone as shown in figure. If the height of the circle above the vertex is 10 cm . The speed of the particle is $\left(\mathrm{g}\right.$, acceleration due to gravity $\left.=10 \mathrm{~m} / \mathrm{s}^2\right)$

Accepted Answer

$$ \begin{aligned} &	ext { From figure, }\ &\begin{array}{ll}  & N \sin 	heta=m g \ & N \cos 	heta=\frac{m V^2}{R} \ 	herefore \quad & 	an 	heta=\frac{R g}{V^2} \ 	herefore \quad & \frac{R}{h}=\frac{R g}{V^2} \ 	herefore \quad & h=\frac{V^2}{g} \ 	herefore \quad & V=\sqrt{h g}=\sqrt{0.1 	imes 10}=1 \mathrm{~m} / \mathrm{s} \end{array} \end{aligned} $$

Answer

$2 \mathrm{~m} / \mathrm{s}$

Answer

$1.5 \mathrm{~m} / \mathrm{s}$

Answer

$1 \mathrm{~m} / \mathrm{s}$

Answer

$0.5 \mathrm{~m} / \mathrm{s}$

Work, Energy and Power & Circular Motion

A particle describes a horizontal circle on smooth inner surface of a cone as shown in figure. If the height of the circle above the vertex is 10 cm . The speed of the particle is \left(\mathrm{g}\right., acceleration due to gravity \left.=10 \mathrm{~m} / \mathrm{s}^2\right)

Choose the correct answer: