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Question

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 ¯¯¯¯¯¯¯¯AB will 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 β is the angle between the 2 sides of the parallelogram)

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