Question 314: Work, Energy and Power & Circular Motion

Question

A particle is moving in a radius $$R$$ with constant speed $$v$$. The magnitude of average acceleration after half revolution is

Accepted Answer

The given situation is shown in the figure.
Change in momentum of particel in half-revolution
$$\Delta p=m v-m(-v)=2 m v \quad 	ext{.... (i)}$$
Time taken by the particle to complete half-revolution,
$$t=\frac{\pi R}{V} \quad 	ext{.... (ii)}$$
$$	herefore$$ Average force $$(F)=$$ Rate of change in momentum
$$\begin{aligned}
& =\frac{\Delta p}{t} \
& =\frac{2 m v}{\pi R / v} \quad 	ext { [From Eqs. (i) and (ii)] } \
F & =\frac{2 m v^2}{\pi R} \Rightarrow m a=\frac{2 m v^2}{\pi R}[F=m a] \
a & =\frac{2 v^2}{\pi R}
\end{aligned}$$

Answer

$$\frac{2 \pi}{R v^2}$$

Answer

$$\frac{2 R}{\pi v}$$

Answer

$$\frac{2 v^2}{\pi R}$$

Answer

$$\frac{2 V}{\pi R^2}$$

Work, Energy and Power & Circular Motion

A particle is moving in a radius $R with constant speed v$. The magnitude of average acceleration after half revolution is

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