If a body moving in a circular path maintains constant speed of 10 ms-1, then which of the following correctly describes relation between acceleration and radius ?

Question

If a body moving in a circular path maintains constant speed of 10 ms-1, then which of the following correctly describes relation between acceleration and radius ? (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Since it is a uniform circular motion, | barν|= constant tangential acceleration aT=0 a=aR=(v2/r) ⇒ a propto (1/r) (Rectangular hyperbola) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/8e97857b2fdfbbcb36e2832177c37e24-.png" />

Q. If a body moving in a circular path maintains constant speed of $10 m s^{- 1}$ , then which of the following correctly describes relation between acceleration and radius ?

Since it is a uniform circular motion, $∣ \overset{ν}{ˉ} ∣ =$ constant tangential acceleration $a_{T} = 0$ $a = a_{R} = \frac{v ^{2}}{r}$
$\Rightarrow a \propto \frac{1}{r}$
(Rectangular hyperbola)

Q. If a body moving in a circular path maintains constant speed of 10ms−1, then which of the following correctly describes relation between acceleration and radius ?

Since it is a uniform circular motion, ∣νˉ∣= constant tangential acceleration aT​=0 a=aR​=rv2​ ⇒a∝r1​ (Rectangular hyperbola)

Q. If a body moving in a circular path maintains constant speed of $10 m s^{- 1}$ , then which of the following correctly describes relation between acceleration and radius ?

Since it is a uniform circular motion, $∣ \overset{ν}{ˉ} ∣ =$ constant tangential acceleration $a_{T} = 0$ $a = a_{R} = \frac{v ^{2}}{r}$
$\Rightarrow a \propto \frac{1}{r}$
(Rectangular hyperbola)