Question

A stone of mass \(40\) g is tied to a light inextensible string of length \(50\) cm and whirled in a vertical circle at the rate of \(30\) revolutions per minute. The tension in the string when it is at the lowest point of the circle is
(Take gravitational acceleration, \(g = 10\,\text{m/s}^2\) and \(π^2 = 10\))

• A. \(0.4\) N
• B. \(0.5\) N
• C. \(0.6\) N
• D. \(0.7\) N

Hint:

At the lowest point the tension must supply the weight plus the centripetal force.

Answer 1

The Correct Option is C

Step 1: Speed route
$v = \omega r = \pi \times 0.5$ m/s, so $v^2 = \pi^2/4 = 2.5$ m$^2$/s$^2$.

Step 2: Newton second law
$T - mg = \dfrac{mv^2}{r}$, so $T = mg + \dfrac{mv^2}{r}$.

Step 3: Substitute
$T = 0.4 + \dfrac{0.04\times2.5}{0.5} = 0.4 + 0.2$.

Step 4: Total
$T = 0.6$ N. The tension is largest at the lowest point because there the weight adds to the centripetal need.

Final Answer:
The tension is 0.6 N. This is option (C). \[ \boxed{\text{(C) }0.6\ \text{N}} \]