B

Step 1: Calculate the initial potential energy (PE) at point A.
The height of point A above point B is equal to the length of the pendulum, which is 2 m. Therefore, the potential energy at point A is given by:
$$ PE = mgh = mg(2) $$
The value of g is 10 m/s², so:
$$ PE = 2mg $$

Step 2: Calculate the energy dissipated due to air resistance.
Given that 10% of the initial potential energy is dissipated, we can find the dissipated energy:
$$ ext{Dissipated energy} = 0.1 imes PE = 0.1 imes 2mg = 0.2mg $$

Step 3: Calculate the final potential energy at point B.
At point B, the potential energy is 0 (since it is the lowest point). Therefore, the remaining mechanical energy at point B after dissipation is:
$$ ext{Remaining energy} = PE - ext{Dissipated energy} = 2mg - 0.2mg = 1.8mg $$

Step 4: Use the remaining energy to calculate the speed at point B.
The remaining energy is converted into kinetic energy (KE) at point B. Therefore:
$$ KE = rac{1}{2} mv^2 $$
Setting this equal to the remaining energy:
$$ rac{1}{2} mv^2 = 1.8mg $$

Step 5: Simplify and solve for v:
Cancelling m from both sides (assuming m ≠ 0):
$$ rac{1}{2} v^2 = 1.8g $$
Hence,
$$ v^2 = 3.6g = 3.6 imes 10 $$
$$ v^2 = 36 $$
$$ v = 6 ext{ m/s} $$

Therefore, the speed with which the bob arrives at the lowermost point B is 6 m/s.