Two forces, \(1\) N and \(2\) N, act along with the lines \(x=0\) and \(y=0\). The equation of the line along which the resultant lies is given by:
1. \(y-2x =0\)
2. \(2y-x =0\)
3. \(y+x =0\)
4. \(y-x =0\)
Component of perpendicular to and in the same plane as that of is:
1.
2.
3.
4.
Given that \(\overrightarrow {C}= \overrightarrow {A}+\overrightarrow {B}\)\(\overrightarrow {C}\) makes an angle \(\alpha\)
1. \(\alpha \) cannot be less than \(\beta\)
2. \(\alpha <\beta, ~\text{if}~A<B\)
3. \(\alpha <\beta, ~\text{if}~A>B\)
4. \(\alpha <\beta, ~\text{if}~A=B\)
If the angle between the vector is , the value of the product is equal to:
1.
2.
3.
4. zero
Two forces A and B have a resultant . If B is doubled, the new resultant is perpendicular to A. Then
1.
2.
3.
4.
Assertion (A): | The graph between \(P\) and \(Q\) is a straight line when \(\frac{P}{Q}\) is constant. |
Reason (R): | The straight-line graph means that \(P\) is proportional to \(Q\) or \(P\) is equal to a constant multiplied by \(Q\). |
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 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°
Two forces with equal magnitudes \(F\) act on a body and the magnitude of the resultant force is \(\frac{F}{3}\). The angle between the two forces is:
1. \(\cos^{- 1} \left(- \frac{17}{18}\right)\)
2. \(\cos^{- 1} \left(- \frac{1}{3}\right)\)
3. \(\cos^{- 1} \left(\frac{2}{3}\right)\)
4. \(\cos^{- 1} \left(\frac{8}{9}\right)\)
Two forces are such that the sum of their magnitudes is \(18~\text{N}\) and their resultant is perpendicular to the smaller force and the magnitude of the resultant is \(12~\text{N}\). Then the magnitudes of the forces will be:
1. \(12~\text{N}, 6~\text{N}\)
2. \(13~\text{N}, 5~\text{N}\)
3. \(10~\text{N}, 8~\text{N}\)
4. \(16~\text{N}, 2~\text{N}\)
If two forces of 5 N each are acting along X and Y axes, then the magnitude and direction of resultant is
(1)
(2)
(3)
(4)