Assertion: A body is making 1 rps in a circle of radius 1 m. Centripetal acceleration acting on it is 4 π2 ms -2. Reason: Centripetal acceleration is given by a =(v2/r)

Question

Assertion: A body is making 1 rps in a circle of radius 1 m. Centripetal acceleration acting on it is 4 π2 ms -2. Reason: Centripetal acceleration is given by a =(v2/r) (A) If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion. (B) If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion. (C) If the Assertion is correct but Reason is incorrect. (D) If the Assertion is incorrect and Reason is correct.

Tardigrade Admin · Accepted Answer

From relation a =(v2/r)=((r ω)2/r)=r ω2 [∵ v = r ω] =r(2 π v)2=4 π2 r v2 Here, v=1 rps , r=1 m ∴ a=4 π2 × 1=4 π2 ms -2

Q. Assertion : A body is making $1 r p s$ in a circle of radius $1 m$ . Centripetal acceleration acting on it is $4 π^{2} m s^{- 2}$ .
Reason : Centripetal acceleration is given by $a = \frac{v ^{2}}{r}$

If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.

If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.

If the Assertion is correct but Reason is incorrect.

If the Assertion is incorrect and Reason is correct.

From relation
$a = \frac{v ^{2}}{r} = \frac{( r ω ) ^{2}}{r} = r ω^{2} [∵ v = r ω]$
$= r (2 π v)^{2} = 4 π^{2} r v^{2}$
Here, $v = 1 r p s, r = 1 m$
$∴ a = 4 π^{2} \times 1 = 4 π^{2} m s^{- 2}$

Q. Assertion : A body is making 1rps in a circle of radius 1m. Centripetal acceleration acting on it is 4π2ms−2. Reason : Centripetal acceleration is given by a=rv2​