Two forces of 3N and 4N are acting on a particle. The forces are acting at an angle of 30∘ between them. The magnitude of the resultant force will be
A
√32+42N
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B
√32+42+3×4cos30N
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C
√32+42+3×4×sin30N
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D
√32+42+2×3×4cos30N
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Solution
The correct option is D√32+42+2×3×4cos30N
The situation mentioned in the question can be depicted by the following figure.
Now to add these two forces we can use parallelogram law of addition of 2 vectors by completing the parallelogram.
The diagonal ¯¯¯¯¯¯¯¯ABwill give the resultant force. |¯¯¯¯¯¯¯¯AB|, the magnitude of the resultant force will be equal to the length of the diagonal which is √(32)+(42)+2(3)(4)cos30. (The length of the diagonal of a parallelogram with sides a and b is √(a2)+(b2)+2(a)(b)cosβ, where βis the angle between the 2 sides of the parallelogram)