In the given figure, represents the total acceleration of a particle moving in the clockwise direction in a circle of radius at a given instant of time. The speed of the particle is [2016]

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Solution

Q.
In the given figure, $a = 15 {ms}^{- 2}$ represents the total acceleration of a particle moving in the clockwise direction in a circle of radius $R = 2.5 m$ at a given instant of time. The speed of the particle is [2016]

1 $4.5 {ms}^{- 1}$

2 $5.0 {ms}^{- 1}$

3 $5.7 {ms}^{- 1}$

4 $6.2 {ms}^{- 1}$

Ans.
(3)

Here, $a = 15 {ms}^{- 2}, R = 2.5 m$

From Figure, $a_{c} = a \cos 30 ° = 15 \times \frac{\sqrt{3}}{2} {ms}^{- 2}$

As we know, $a_{c} = \frac{v^{2}}{R} \Rightarrow v = \sqrt{a_{c} R}$

$∴ v = \sqrt{15 \times \frac{\sqrt{3}}{2} \times 2.5} = 5.69 ≃ 5.7 {ms}^{- 1}$

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