Question

a ball weighing 100 g is attached to a string and swung around with a speed of 2 m/s. if the centripetal force exerted by the string is 0.5 n, what is the length of the string?
a 0.08 m
b 0.8 cm
c 8 m
d 80 cm

Explanation:

Step1: Recall Centripetal Force Formula

The centripetal force formula is \( F = \frac{mv^2}{r} \), where \( F \) is centripetal force, \( m \) is mass, \( v \) is velocity, and \( r \) is the radius (length of the string here). First, convert mass to kg: \( m = 100\ \text{g} = 0.1\ \text{kg} \), \( v = 2\ \text{m/s} \), \( F = 0.5\ \text{N} \).

Step2: Rearrange Formula for \( r \)

From \( F = \frac{mv^2}{r} \), solve for \( r \): \( r = \frac{mv^2}{F} \).

Step3: Substitute Values

Substitute \( m = 0.1\ \text{kg} \), \( v = 2\ \text{m/s} \), \( F = 0.5\ \text{N} \) into the formula:
\( r = \frac{0.1 \times (2)^2}{0.5} = \frac{0.1 \times 4}{0.5} = \frac{0.4}{0.5} = 0.8\ \text{m} \)? Wait, no, wait—wait, 0.8 m is 80 cm? Wait, no, let's recalculate. Wait, \( 0.1 \times 4 = 0.4 \), divided by 0.5 is 0.8? Wait, but the options: A is 0.08 m, B is 0.8 cm, C is 8 m, D is 80 cm (which is 0.8 m). Wait, maybe I made a mistake. Wait, mass is 100 g = 0.1 kg, velocity 2 m/s, force 0.5 N. So \( r = \frac{mv^2}{F} = \frac{0.1 \times 4}{0.5} = \frac{0.4}{0.5} = 0.8\ \text{m} \), which is 80 cm (since 1 m = 100 cm, 0.8 m = 80 cm). So the length is 0.8 m or 80 cm, which is option D? Wait, no, wait the options: A is 0.08 m, B is 0.8 cm, C is 8 m, D is 80 cm. Let's check units again. \( F = 0.5\ \text{N} \), \( m = 0.1\ \text{kg} \), \( v = 2\ \text{m/s} \). So \( r = \frac{mv^2}{F} = \frac{0.1 \times 4}{0.5} = 0.8\ \text{m} = 80\ \text{cm} \), which matches option D.

Answer:

D. 80 cm