A

Step 1: Analyze the Forces
When the person pulls the mass 'm' from the ground to the top of the hemisphere, we need to consider two primary forces acting on the mass 'm':

• The gravitational force: $F_g = mg = 1 ext{ kg} \times 10 ext{ m/s}^2 = 10 ext{ N}$.
• The frictional force due to the rough surface: $F_f = \mu N$, where $N$ is the normal force. Here, $N = mg$ at the bottom (horizontal surface) due to the vertical pull.

Since the coefficient of friction ($\mu$) is 0.1, the frictional force can be calculated as $F_f = 0.1 \times 10 ext{ N} = 1 ext{ N}$.

Step 2: Calculate the Distance
The distance d that the mass 'm' moves can be visualized as the height of the hemisphere, which equals the radius, $R=1 ext{ m}$.

Step 3: Calculate the Work Done
The work done by the tension in the string can be calculated using the equation:
$$ W = F_{tension} \times d $$
Where $F_{tension}$ compensates for the work done against gravitational force and friction:
$$ F_{tension} = F_g + F_f = 10 ext{ N} + 1 ext{ N} = 11 ext{ N} $$
The work done by the tension is:
$$ W = 11 ext{ N} \times 1 ext{ m} = 11 ext{ J} $$
Therefore, the work done by the tension in the string on the mass 'm' is 11 Joules.