Question

A body moves along a circular path of the radius $5 \, m$ . The coefficient of friction between the surface of the path and the body is $ \, 0.5$ . The angular velocity in $rad \, s^{- 1}$ , with which the body should move so that it does not have to leave the path is (Take $g=10 \, m \, s^{- 2}$ )

• A. $4$
• B. $3$
• C. $2$
• D. $1$

Answer 1

Answer: (D)

Here, $\mu = \text{0.5}$
r = 5 m, g = 10 m s^-2
The friction force provides the centripetal force
$∴ \, \, \frac{\text{mv}^{2}}{\text{r}} = \mu \text{mg}$ or $\text{v}^{2} = \mu \text{rg}$
or or $\mathrm{v}=\sqrt{\mu \mathrm{rg}}=\sqrt{(0.5)(5 \mathrm{~m})\left(10 \mathrm{~m} \mathrm{~s}^{-2}\right)}$
$= 5 \text{ m s}^{- 1}$
As $\text{v} = \text{r} \omega $ or $\omega = \frac{\text{v}}{\text{r}} = \frac{5 \text{ m s}^{- 1}}{5 \text{ m}} = 1 \text{ rad s}^{- 1}$