Question 132: Work, Energy and Power & Circular Motion

Question

A bead of mass m stays at point P(a, b) on a
wire bent in the shape of a parabola y = 4Cx
2
and rotating with angular speed $$\omega $$ (see figure).
The value of $$\omega $$ is (neglect friction) :

Accepted Answer

y = 4Cx
2
$$ \Rightarrow $$ $$\frac{dy}{dx}  $$ = tan $$	heta $$ = 8Cx
At P, tan ÃÂ¸ = 8Ca
For steady circular motion
mg sinÃÂ¸ = mÃÂ
2
acosÃÂ¸
$$ \Rightarrow $$ tan $$	heta $$ = $$\frac{\omega^{2} a}{g} $$
$$ \Rightarrow $$ 8Ca $$ 	imes $$ g = ÃÂ
2
$$ 	imes $$a
$$ \Rightarrow $$ $$\omega $$ = $$\sqrt{8gC} $$
$$ \Rightarrow $$ $$\omega $$ = $$2\sqrt {2gC} $$

Answer

$$2\sqrt {2gC} $$

Answer

$$2\sqrt {gC} $$

Answer

$$\sqrt {{{2gC} \over {ab}}} $$

Answer

$$\sqrt {{{2g} \over C}} $$

Work, Energy and Power & Circular Motion

A bead of mass m stays at point P(a, b) on a wire bent in the shape of a parabola y = 4Cx 2 and rotating with angular speed $\omega (see figure). The value of \omega $ is (neglect friction) :

Choose the correct answer: