Assertion -Velocity and acceleration of a particle in circular motion at some instant are- v- 2- ms-1 and a- -2- ms-2- then radius of circle is 2 m- Reason- Speed of particle is decreasing at a rate of 1 ms-2-

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Assertion :Ve...

Question

Assertion :Velocity and acceleration of a particle in circular motion at some instant are: $\to v = (2^i) m s^{- 1} a n d \to a = (-^i + 2^j) m s^{- 2},$ then radius of circle is $2$ m. Reason: Speed of particle is decreasing at a rate of $1 m s^{- 2} .$

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Both Assertion is incorrect and Reason is correct

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Solution

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
$\to v = (2^i) m s^{- 1} \to a = (-^i + 2^j) m s^{- 2} W e k n o w, a_{j} = \frac{v_{i}^{2}}{r} r = \frac{4}{2} = 2$

Hence, assertion is correct. Speed of the particle is decreasing due to a negative acceleration over x axis which has a magnitude of $1 m s^{- 2}$ . Hence, reason is correct. But, radius of circle is calculated by using the radial acceleration and hence reason does not explain assertion in this case.

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Assertion :Velocity and acceleration of a particle in circular motion at some instant are: →v=(2^i)ms−1and→a=(−^i+2^j)ms−2, then radius of circle is 2 m. Reason: Speed of particle is decreasing at a rate of 1ms−2.

Assertion :Velocity and acceleration of a particle in circular motion at some instant are: $\to v = (2^i) m s^{- 1} a n d \to a = (-^i + 2^j) m s^{- 2},$ then radius of circle is $2$ m. Reason: Speed of particle is decreasing at a rate of $1 m s^{- 2} .$