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Two forces are such that the sum of their magnitudes is 18 N and their resultant is 12 N which is perpendicular to the smaller force. Then the magnitudes of the forces are
- a)12 N, 6 N
- b)13 N, 5 N
- c)10 N, 8 N
- d)16N, 2N.
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two forces are such that the sum of their magnitudes is 18 N and their...
Let the two forces be F1 and F2 and let F2 < F1 . R is the resultant force.
Given F1 + F2 = 18 ...(i)
Only option (b) follows equation (i) and (ii).
Most Upvoted Answer
Two forces are such that the sum of their magnitudes is 18 N and their...
The resultant And the two forces form a right angled triangle. This Pythagoras theorem must be followed. The resultant is 12, which is perpendicular to the smaller force. But as we know the hypotenuse is not perpendicular to any of the other two sides, it's clear that the smaller force and the resultant of 12 N form the base and height our vice versa. So (hyp)^2 - (smaller force)^2 = 144.
Way 1 :All the options have their sum as 18. So check the options such that the square of first - square of second is 144. It's only option B
Alternative:
Now sum of magnitude of the forces is 18. Let the smaller be x so larger one is 18-x.
So the quadratic equation becomes (18-x)^2 - x^2 = 144. On solving we get x=5. So the other one is 13.
Way 1 :All the options have their sum as 18. So check the options such that the square of first - square of second is 144. It's only option B
Alternative:
Now sum of magnitude of the forces is 18. Let the smaller be x so larger one is 18-x.
So the quadratic equation becomes (18-x)^2 - x^2 = 144. On solving we get x=5. So the other one is 13.
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Two forces are such that the sum of their magnitudes is 18 N and their resultant is 12 N which is perpendicular to the smaller force. Then the magnitudes of the forces area)12 N, 6 Nb)13 N, 5 Nc)10 N, 8 Nd)16N, 2N.Correct answer is option 'B'. Can you explain this answer?
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