Question

A body with a mass of 2 kg and a weight of 20 N is travelling in a vertical circular motion with a radius of 1 m and a velocity of 5 m/s. When the string is horizontal, what is the tension?

• A. 30 N
• B. 50 N
• C. 20 N
• D. 25 N

Answer 1

Answer: (B)

50 N

Answer 2

Understanding the Setup: A body is undergoing vertical circular motion. We need to find the tension in the string when the string is horizontal.

Given Values:

• Mass of the body, $m = 2$ kg
• Radius of the circular path, $r = 1$ m
• Velocity of the body when the string is horizontal, $v = 5$ m/s
• Weight of the body, $W = 20$ N. From $W = mg$, we can find $g = W/m = 20 \text{ N} / 2 \text{ kg} = 10 \text{ m/s}^2$.

Forces at the Horizontal Position:

When the string is horizontal, the forces acting on the body are:

1. Tension (T): Acts horizontally towards the center of the circle and provides the centripetal force.
2. Weight (mg): Acts vertically downwards.

Applying Newton's Second Law:

The centripetal force ($F_c$) required for circular motion is given by: $F_c = \frac{mv^2}{r}$

At the horizontal position, the tension (T) provides this centripetal force: $T = F_c$ $T = \frac{mv^2}{r}$

Calculation:

Substitute the given values into the equation: $T = \frac{(2 \text{ kg}) \times (5 \text{ m/s})^2}{1 \text{ m}}$ $T = \frac{2 \times 25}{1}$ $T = 50 \text{ N}$

The tension in the string when it is horizontal is 50 N.