Question 261: Work, Energy and Power & Circular Motion

Question

A body of mass 200 gram is tied to a spring of spring constant $$12.5 \mathrm{~N} / \mathrm{m}$$, while other end of spring is fixed at point '$$O$$'. If the body moves about '$$O$$' in a circular path on a smooth horizontal surface with constant angular speed $$5 \mathrm{~rad} / \mathrm{s}$$ then the ratio of extension in the spring to its natural length will be

Accepted Answer

Let the normal length be $$\mathrm{L}$$ and the extension be $$\mathrm{x}$$.
$$	herefore \quad$$ Restoring Force $$=$$ Centripetal Force
$$\begin{aligned}
& \mathrm{kx}=\mathrm{m}(\mathrm{L}+\mathrm{x}) \omega^2 \
& 12.5 \mathrm{x}=0.2(\mathrm{~L}+\mathrm{x}) 25 \quad \ldots(\because \omega=5 \mathrm{~rad} / \mathrm{s})
\end{aligned}$$
$$\begin{aligned}
& 12.5 x=5(L+x) \
& 7.5 x=5 L \
	herefore \quad & \frac{x}{L}=\frac{5}{7.5}=\frac{2}{3}=2: 3
\end{aligned}$$

Answer

1 : 2

Answer

1 : 1

Answer

2 : 3

Answer

2 : 5

Work, Energy and Power & Circular Motion

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