A body is moving along a circular path of radius ' r ' with a frequency of revolution numerically equal to the radius of the circular path. What is the acceleration of the body if radius of the path is (‌
First, let's analyze the given information. The radius of the circular path, r, is given as ‌
5
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meters. The frequency of revolution, f, is numerically equal to the radius, so f=r=‌
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‌Hz. The acceleration we need to find is the centripetal acceleration, which is given by the formula: a=ω2r Here, ω (omega) is the angular velocity, which can be calculated from the frequency f using the relationship: ω=2πf Substitute f=‌
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into the equation for ω : ω=2π(‌
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)=10‌rad∕s Now, substitute ω=10‌rad∕s and r=‌
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meters into the centripetal acceleration formula: a=ω2r=(10)2(‌
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) Thus, the acceleration a is: a=100(‌
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)=‌
500
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m∕s2 Therefore, the correct option is: Option D: (‌