That's question 46 solve it in English

• Mass of the ball, $m = 0.4 \, \text{kg}$.
• Length of the string (which is the radius of the circular path), $r = 0.8 \, \text{m}$.
• Speed of the ball at the lowest point, $v = 6.0 \, \text{m/s}$.
• Acceleration due to gravity, $g = 9.8 \, \text{m/s}^2$.

At the lowest point of the vertical circle, two forces act on the ball:

1. The tension ($T$) in the string, acting upwards (towards the center of the circle).
2. The gravitational force ($mg$), acting downwards (away from the center of the circle).

The net force acting towards the center of the circle provides the centripetal force ($F_c$). At the lowest point, the centripetal force is the difference between the tension and the gravitational force.

$$F_{\text{net}} = T - mg$$

The centripetal force is given by $F_c = \frac{mv^2}{r}$.
Equating the net force to the centripetal force:

$$T - mg = \frac{mv^2}{r}$$

Rearrange the equation to isolate $T$:

$$T = mg + \frac{mv^2}{r}$$

Substitute the given numerical values into the equation:

$$T = (0.4 \, \text{kg})(9.8 \, \text{m/s}^2) + \frac{(0.4 \, \text{kg})(6.0 \, \text{m/s})^2}{0.8 \, \text{m}}$$

First, calculate the gravitational force:

$$mg = 0.4 \times 9.8 = 3.92 \, \text{N}$$

Next, calculate the centripetal force term:

$$\frac{mv^2}{r} = \frac{0.4 \times (6.0)^2}{0.8} = \frac{0.4 \times 36}{0.8} = \frac{14.4}{0.8} = 18 \, \text{N}$$

Now, add these two values to find the tension:

$$T = 3.92 \, \text{N} + 18 \, \text{N}$$ $$T = 21.92 \, \text{N}$$

Rounding $21.92 \, \text{N}$ to two significant figures (consistent with the input values) gives $22 \, \text{N}$.
The given options are:
(A) 4.0 N
(B) 14 N
(C) 18 N
(D) 22 N

The calculated tension matches option (D).

The final answer is $\boxed{\text{D}}$.