The resultant of two forces acting at right angles is $$\sqrt {34} \,$$ kg and acting at 60° is 70 kg. The forces are A. 1 kg and 4 kg B. 2 kg and 3 kg C. $$\sqrt 3 $$ kg and $$\sqrt 5 $$ kg D. 3 kg and 5 kg

[amp_mcq option1=”1 kg and 4 kg” option2=”2 kg and 3 kg” option3=”$$\sqrt 3 $$ kg and $$\sqrt 5 $$ kg” option4=”3 kg and 5 kg” correct=”option1″]

The correct answer is $\boxed{\text{C. }\sqrt{3} \,\text{ kg and }\sqrt{5} \,\text{ kg}}$.

Let $F_1$ and $F_2$ be the two forces. We know that $F_1^2 + F_2^2 = (\sqrt{34})^2$ and $F_1F_2 = 70$. We can solve this system of equations to find $F_1 = \sqrt{3}$ and $F_2 = \sqrt{5}$.

Here is a brief explanation of each option:

• Option A: $1 \,\text{ kg and }4 \,\text{ kg}$. This is not possible because the sum of two forces cannot be a square root.
• Option B: $2 \,\text{ kg and }3 \,\text{ kg}$. This is not possible because the sum of two forces cannot be a square root.
• Option C: $\sqrt{3} \,\text{ kg and }\sqrt{5} \,\text{ kg}$. This is possible because the sum of two forces can be a square root.
• Option D: $3 \,\text{ kg and }5 \,\text{ kg}$. This is not possible because the sum of two forces cannot be a square root.