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 π2 N. Reason: Centrifugal force is given by F=(m v2/r)

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 π2 N. Reason: Centrifugal force is given by F=(m v2/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.

Tardigrade Admin · Accepted Answer

From relation F =(m v2/r)=(m(r ω)2/r)=m r ω2 =m r(2 π v)2 4 π2 m r v2 Here, m=1 kg v=1 rps , r=1 m ∴ F=4 π2 × 1 × 1 × 12=4 π2 N

Q. Assertion : A body of mass $1 k g$ is making $1 r p s$ in a circle of radius $1 m$ . Centrifugal force acting on it is $4 π^{2} N$ .
Reason : Centrifugal force is given by $F = \frac{m v ^{2}}{r}$

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

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

If Assertion is true but Reason is false.

If both Assertion and Reason are false.

From relation
$F = \frac{m v ^{2}}{r} = \frac{m ( r ω ) ^{2}}{r} = m r ω^{2}$
$= m r (2 π v)^{2} 4 π^{2} m r v^{2}$
Here, $m = 1 k gv = 1 r p s, r = 1 m$
$∴ F = 4 π^{2} \times 1 \times 1 \times 1^{2} = 4 π^{2} N$

Q. Assertion : A body of mass 1kg is making 1rps in a circle of radius 1m. Centrifugal force acting on it is 4π2N. Reason : Centrifugal force is given by F=rmv2​