Question

Assertion : A body of mass $1\, kg$ is making $1 \,rps$ in a circle of radius $1\, m$. Centrifugal force acting on it is $4 \pi^{2} N$.
Reason : Centrifugal force is given by $F=\frac{m v^{2}}{r}$

• A. If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
• B. If both Assertion and Reason are true but the Reason is not the correct explanation of the Assertion.
• C. If Assertion is true but Reason is false.
• D. If both Assertion and Reason are false.

Answer 1

Answer: (A)

From relation
$F =\frac{m v^{2}}{r}=\frac{m(r \omega)^{2}}{r}=m r \omega^{2} $
$=m r(2 \pi v)^{2} 4 \pi^{2} m r v^{2}$
Here, $m=1 \,kg v=1 \,rps , r=1\, m$
$\therefore F=4 \pi^{2} \times 1 \times 1 \times 1^{2}=4 \pi^{2} N$