1. Given data

• Mass of the object: $100\text{ g} = 0.1\text{ kg}$
• Force on the object: $\vec F = 10\hat i + 5\hat j \;\text{N}$
• Initial velocity: object starts from rest, so $\vec u = 0$
• Time: $t=2\text{ s}$

2. Find acceleration using Newton's second law

Using $\vec F = m\vec a$ we get $\vec a = \frac{\vec F}{m} = \frac{10\hat i + 5\hat j}{0.1}$

So, $\vec a = 100\hat i + 50\hat j \;\text{m/s}^2$

3. Find displacement after 2 s

Since initial velocity is zero, $\vec r = \vec u t + \frac{1}{2}\vec a t^2 = \frac{1}{2}\vec a t^2$

At $t=2$ s, $\vec r = \frac{1}{2}(100\hat i + 50\hat j)(2)^2$

$\vec r = \frac{1}{2}(100\hat i + 50\hat j)\cdot 4$

$\vec r = 2(100\hat i + 50\hat j)$

$\vec r = 200\hat i + 100\hat j$

Hence, $a=200,\qquad b=100$

4. Calculate $\dfrac{a}{b}$

$\frac{a}{b} = \frac{200}{100} = 2$

5. Comparison with stored answer

Derived answer is $2$, which matches the stored correct answer.