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

To determine the string tension at the stone's lowest point, analyze the forces involved in its circular motion.

Required parameters are:

• Stone mass, \(m = 0.9 \, \text{kg}\)
• Circular radius, \(r = 1 \, \text{m}\)
• Rotations per minute, \(N = 10 \, \text{rpm}\)
• Gravitational acceleration, \(g = 9.8 \, \text{m/s}^{2}\)

At the circle's lowest point, forces acting on the stone include string tension \( T \) and gravitational force. The net centripetal force is the difference between tension and gravity:

\(T - mg = m \omega^2 r\)

Where \( \omega \) is angular velocity in radians per second. Convert rpm to rad/s:

\(\omega = \frac{2\pi N}{60} \, \text{rad/s}\)

\(\omega = \frac{2 \times 3.14 \times 10}{60} \approx 1.047 \, \text{rad/s}\)

Substitute \( \omega \) back into the centripetal force equation:

\(T = mg + m \omega^2 r\)

Calculate individual components:

• \(mg = 0.9 \times 9.8 = 8.82 \, \text{N}\)
• \(m \omega^2 r = 0.9 \times (1.047)^2 \times 1 \approx 0.99 \, \text{N}\)

Sum these for total tension:

\(T = 8.82 + 0.99 = 9.81 \, \text{N}\)

Rounding based on significant figures yields:

Correct Answer: 9.8 N