In a given figure (assume standard representation), $a=20 \mathrm{~m} \mathrm{~s}^{-2}$ represents t

Question

In a given figure (assume standard representation), $a=20 \mathrm{~m} \mathrm{~s}^{-2}$ represents the total acceleration of a particle moving in the clockwise direction in a circle of radius $R=2.0 \mathrm{~m}$ at a given instant of time. If the acceleration vector makes an angle of $60^{\circ}$ with the radius vector towards the centre, the speed of the particle is

Professor PC Thomas Classes · Answer

(a) : Here, $a=20 \mathrm{~m} \mathrm{~s}^{-2}, R=2.0 \mathrm{~m}$. \ Centripetal acceleration is the radial component: $a_{c}=a \cos 60^{\circ}=20 	imes \frac{1}{2} = 10 \mathrm{~m} \mathrm{~s}^{-2}$. \ As we know, $a_{c}=\frac{v^{2}}{R} \Rightarrow v=\sqrt{a_{c} R}$ \ $	herefore \quad v=\sqrt{10 	imes 2.0} = \sqrt{20} \approx 4.47 \simeq 4.5 \mathrm{~m} \mathrm{~s}^{-1}$