Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

In the given figure, $a=15 \text{ m/s}^2$ represents the total acceleration of a particle moving in the clockwise direction in a circle of radius $R=2.5 \text{ m}$ at a given instant of time. The speed of the particle is:

4.5 m/s

5.0 m/s

5.7 m/s

6.2 m/s

Step-by-Step Solution

Centripetal Acceleration Component: The particle moves in a circle, so it possesses centripetal acceleration ( $a_c$ ) directed towards the center. The given total acceleration $a$ has a radial component ( $a_c$ ) and a tangential component ( $a_t$ ). Based on the standard representation of this specific problem (NEET 2016), the total acceleration vector makes an angle of $30^{\circ}$ with the radius vector.
Formula: The radial component is $a_c = a \cos \theta$ .
Speed Relationship: Centripetal acceleration is defined as $a_c = \frac{v^2}{R}$ .
Calculation: $\frac{v^2}{R} = a \cos 30^{\circ}$ Substituting given values ( $a=15, R=2.5$ ): $\frac{v^2}{2.5} = 15 \times \frac{\sqrt{3}}{2}$ $v^2 = 2.5 \times 15 \times 0.866 \approx 32.475$ $v = \sqrt{32.475} \approx 5.7 \text{ m/s}$

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