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Answer :
Final Answer:
The radial acceleration, calculated using [tex]\( a_r = \frac{v^2}{r} \)[/tex], where [tex]\( v = 4\pi \)[/tex] m/s and ( r = 2 ) m, yields approximately 36 m/s². The correct option is c.
Explanation:
To find the magnitude of the radial acceleration, we use the formula for radial acceleration: [tex]\( a_r = \frac{v^2}{r} \)[/tex], where ( v ) is the velocity and ( r ) is the radius of the circle. Given the period of rotation ( T = 1 ) second, we can find the velocity ( v ) using the formula for the velocity of an object in circular motion: [tex]\( v = \frac{2\pi r}{T} \)[/tex]. Substituting the given values, we get [tex]\( v = \frac{2 \times \pi \times 2}{1} = 4\pi \)[/tex] m/s. Now, substituting ( v ) and ( r = 2 ) meters into the formula for radial acceleration, we obtain [tex]\( a_r = \frac{(4\pi)^2}{2} = 16\pi^2 \)[/tex] m/s². Since [tex]\( \pi \)[/tex] is approximately 3.14, [tex]\( 16\pi^2 \)[/tex] is approximately [tex]\( 16 \times 3.14^2 = 36.0156 \)[/tex] m/s², which rounds to 36 m/s².
Therefore, the magnitude of the radial acceleration is approximately 36 m/s². This acceleration represents the rate of change of velocity of the stone as it moves in a circular path. It indicates the force exerted by the tension in the cord, which keeps the stone moving in a circular motion despite the gravitational force acting on it.
Thus, option c. 36 is the correct choice.
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