Question 213: Work, Energy and Power & Circular Motion

Question

A body performing uniform circular motion of radius ' $R$ ' has frequency ' $n$ '. Its centripetal acceleration per unit radius is proportional to $(n)^x$. The value of $x$ is

Accepted Answer

Let's break down the problem step by step:
For a body in uniform circular motion, the tangential speed is given by:
$$v = 2\pi R n$$
where:
$$R$$ is the radius,
$$n$$ is the frequency (number of revolutions per unit time).
The centripetal acceleration is given by:
$$a = \frac{v^2}{R}.$$
Substituting the expression for $$v$$ into the acceleration formula:
$$a = \frac{(2\pi R n)^2}{R} = \frac{4\pi^2 R^2 n^2}{R} = 4\pi^2 n^2 R.$$
The centripetal acceleration per unit radius is therefore:
$$\frac{a}{R} = \frac{4\pi^2 n^2 R}{R} = 4\pi^2 n^2.$$
This shows that the centripetal acceleration per unit radius is directly proportional to $$n^2$$. Hence, the exponent $$x$$ is 2.
So, the answer is: Option B (2).

Answer

1

Answer

2

Answer

$-$1

Answer

$-$2

Work, Energy and Power & Circular Motion

A body performing uniform circular motion of radius ' R ' has frequency ' n '. Its centripetal acceleration per unit radius is proportional to (n)^x. The value of x is

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