If the magnitude of the sum of two vectors is equal to the magnitude of the difference between the two vectors, the angle between these vectors is:
1. 90∘90∘
2. 45∘45∘
3. 180∘180∘
4. 0∘0∘
If vectors A = cosωt ˆiˆi + sinωt ˆjˆj and B = (cosωt/2) ˆiˆi + (sinωt/2) ˆjˆj are functions of time, then the value of t at which they are orthogonal to each other
1. t=ππ/4ω
2. t=ππ/2ω
3. t=ππ/ω
4. t=0
Six vectors →a through →f→a through →f have the directions as indicated in the figure. Which of the following statements may be true?
1. →b+→c=−→f→b+→c=−→f
2. →d+→c=→f→d+→c=→f
3. →d+→e=→f→d+→e=→f
4. →b+→e=→f→b+→e=→f
If two forces of 5 N each are acting along X and Y axes, then the magnitude and direction of resultant is
1. 5√2, π/35√2, π/3
2. 5√2, π/45√2, π/4
3. −5√2, π/3−5√2, π/3
4. −5√2, π/4−5√2, π/4
Two forces are such that the sum of their magnitudes is 18 N18 N and their resultant is perpendicular to the smaller force and the magnitude of the resultant is 12 N12 N. Then the magnitudes of the forces will be:
1. 12 N,6 N12 N,6 N
2. 13 N,5 N13 N,5 N
3. 10 N,8 N10 N,8 N
4. 16 N,2 N16 N,2 N
Two forces with equal magnitudes FF act on a body and the magnitude of the resultant force is F3F3. The angle between the two forces is:
1. cos−1(−1718)cos−1(−1718)
2. cos−1(−13)cos−1(−13)
3. cos−1(23)cos−1(23)
4. cos−1(89)cos−1(89)
Two forces of magnitude F have a resultant of the same magnitude F. The angle between the two forces is
1. 45°
2 120°
3. 150°
4. 60°
Assertion (A): | The graph between PP and QQ is a straight line when PQPQ is constant. |
Reason (R): | The straight-line graph means that PP is proportional to QQ or PP is equal to a constant multiplied by QQ. |
1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
3. | (A) is True but (R) is False. |
4. | Both (A) and (R) are False |
Two forces A and B have a resultant R1R1. If B is doubled, the new resultant R2R2 is perpendicular to A. Then
1. R1=AR1=A
2. R1=BR1=B
3. R2=AR2=A
4. R2=BR2=B