Question

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

• 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.

Answer 1

Answer: (A)

From relation
$ a =\frac{v^2}{r}=\frac{(r \omega)^2}{r}=r \omega^2 [\because v = r \omega]$
$=r(2 \pi v)^2=4 \pi^2 r v^2$
Here, $v=1 \, rps , r=1\, m$
$\therefore a=4 \pi^2 \times 1=4 \pi^2\, ms ^{-2}$