One of the two forces is double the other and their resultant is equal to the greater force.The angle between them is
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Vectors mcqs
Physics class 11th mcqs
First year physics mcqs
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00:00The question is, one of the two forces is double the other, and their resultant is equal
00:12to the greater force, the angle between them is, a, cos inverse 1 upon 2, b, cos inverse
00:21minus 1 upon 2, c, cos inverse 1 upon 4, d, cos inverse minus 1 upon 4, is according to
00:34condition, F1 is equal to F, and F2 is equal to 2F, because, here it is given as, one of
00:51the two forces is double the other, and their resultant is equal to the greater force, so
01:00the second force is double than the first force, and resultant is also equal to the
01:07larger force, means greater force, means 2F, so R is equal to 2F, so by using law of cosine,
01:20R is equal to, under root, F1 square plus, F2 square plus, 2F1, F2, cos theta, here resultant
01:43is equal to 2F, so 2F will be equal to, under root, F1 is equal to F, so square on F, plus
01:55F2 is equal to 2F, so 2F whole square plus, 2 into F, into 2F, cos theta, because F2 is
02:12equal to 2F, so 2F will be equal to, under root, F square plus, the square of 2F is 4,
02:32F square plus, 2 into 2, it will be 4, F into F, it will be, F square, cos theta, so
02:43to remove square root, squaring on, both sides, so it will be, 4F square is equal to, is F
02:58square plus, 4F square, it will be, 5F square, plus, 4F square, cos theta, so 4F square,
03:17when we will take 5F square, on the other side of equal, then it will be minus, 5F square,
03:26is equal to, 4F square, cos theta, so 4F square minus, 5F square, it will be minus,
03:37F square is equal to, here 4F square is multiplying with, cos theta, so on the other side of the
03:43equal, it will divide, so it will be, minus F square upon, 4F square is equal to, cos
03:51theta, so F square will be, get cancelled with F square, so minus 1 upon 4, is equal
03:57to, cos theta, or we can also write it as, cos theta is equal to, minus 1 upon 4, so
04:11we have to find angle, so theta will be equal to, cos inverse, minus, 1 upon 4, so the correct
04:21option will be, d cos inverse, minus 1 upon 4.