Question

A stone of mass 900 g is tied to a string and moved in a vertical circle of radius 1 m making 10 rpm. The tension in the string, when the stone is at the lowest point, is (if \( \pi^2 = 9.8 \) and \( g = 9.8 \, \text{m/s}^2 \))

• A. 97 N
• B. 9.8 N
• C. 8.82 N
• D. 17.8 N

Answer 1

The Correct Option is B

Given:  
- Mass of the stone, \( m = 900 \, \text{g} = 0.9 \, \text{kg} \)  
- Radius of the circle, \( r = 1 \, \text{m} \)  
- Angular velocity in rpm, \( \omega = 10 \, \text{rpm} \)

Step 1. Convert rpm to rad/s:  
  
  \(\omega = 10 \times \frac{2\pi}{60} = \frac{\pi}{3} \, \text{rad/s}\)
  \]

Step 2. Calculate the centripetal force at the lowest point:  
  The centripetal force \( F_c = m\omega^2r \):  
 
  \(F_c = 0.9 \times \left(\frac{\pi}{3}\right)^2 \times 1 = 0.9 \times \frac{\pi^2}{9} = 0.9 \times \frac{9.8}{9} = 0.98 \, \text{N}\)
 
Step 3. Calculate the tension \( T \) at the lowest point:  
  At the lowest point, the tension \( T \) in the string must support both the gravitational force and the centripetal force. Thus:  
  \(T = mg + F_c\)
 \(T = (0.9 \times 9.8) + 0.98 = 8.82 + 0.98 = 9.8 \, \text{N}\)
Thus, the tension in the string at the lowest point is 9.8 N.

The Correct Answer is: 9.8 N