Mathematics - Statics

Question - 1

The resultant of two forces P and Q is R. If Q is doubled,then R is doubled. If direction of Q is reversed, R is doubled again, then \({ P }^{ 2 }:{ Q }^{ 2 }:{ R }^{ 2 }\)is:

  • A 2:3:2
  • B 1:2:3
  • C 2:3:1
  • D 3:1:1

Question - 2

If the resultant of two forces of magnitudes P and 2P is perpendicular to P, then the angle between the forces, is 

  • A \(\frac { 2\Pi }{ 3 } \)
  • B \(\frac { 3\Pi }{ 4 } \)
  • C \(\frac { 4\Pi }{ 5 } \)
  • D \(\frac { 5\Pi }{ 6 } \)

Question - 3

The resultant of two forces P and Q acting an angle \(\alpha \) is equal to \((2m+1)\sqrt { { P }^{ 2 }+{ Q }^{ 2 } } \) and when these forces act at an angle \(({ 90 }^{ \circ }-\alpha )\), the result is \((2m+1)\sqrt { { P }^{ 2 }+{ Q }^{ 2 } } \). then,\(\tan { \alpha } \) equals

  • A \(\frac { m+1 } {m-1 }\)
  • B \(\frac { m } {m+1 }\)
  • C \(\frac { m-1 } {m+1 }\)
  • D \(\frac { m } {m-1 }\)

Question - 4

Two forces P and Q acting at a point are such that if one of these is reversed, the direction of the resultant is turned through a right angle, then

  • A P=2Q
  • B 2P=Q
  • C 2P=3Q
  • D P=Q

Question - 5

Two forces P+Q and P-Q make an angle  2\(\alpha \) with each other and their resultant makes an angles \(\theta \) with the bisector of the angle between them, then

  • A \(P\quad \tan { \theta } =Q\quad \tan { \alpha } \)
  • B \(P\quad \tan { \alpha } =Q\quad \tan { \theta } \)
  • C \(P\quad \tan { (\alpha +\theta ) } =Q\quad \tan { (\alpha } -\theta )\)
  • D None of these

Question - 6

If the resultant of two equal forces inclined at an angle \(2{\theta}\) is twice as grest as when these are inclined at an angle \(2\Phi \),then

  • A \(2\cos { \theta } =\cos { \phi } \)
  • B \(\cos { \theta } =2\cos { \phi } \)
  • C \(\theta =\Pi \)
  • D None of these

Question - 7

The greatest resultant of two forces is P and least resultant is Q. when these forces act an angle \(\theta\), then the resultant ,is

  • A \(\sqrt { ({ P }^{ 2 }{ sin }^{ 2 }(\frac { \theta }{ 2 } )+{ Q }^{ 2 }{ cos }^{ 2 }(\frac { \theta }{ 2 } ) } \)
  • B \(\sqrt { ({ P }^{ 2 }{ +Q }^{ 2 } } \)
  • C \(\sqrt { { P }^{ 2\quad }{ cos }^{ 2 }(\frac { \theta }{ 2 } )+{ Q }^{ 2 }{ sin }^{ 2 }(\frac { \theta }{ 2 } ) } \)
  • D None of these

Question - 8

The resultant of two forces P and Q is \(\sqrt { 3 }\)Q and makes an angle \({ 30 }^{ \circ }\)with the direction of P. then

  • A P=Q or P=2Q
  • B P=Q or Q=2P
  • C P=2Q or Q=3P
  • D P=Q or P=4Q

Question - 9

The resultant R of two forces P and Q act at right angles to P. Then the angle between these forces, is

  • A \({ cos }^{ -1 }(\frac { P }{ Q } )\)
  • B \({ cos }^{ -1 }(-\frac { P }{ Q } )\)
  • C \({ sin }^{ -1 }(\frac { P }{ Q } )\)
  • D \({ sin }^{ -1 }(-\frac { P }{ Q } )\)

Question - 10

If the resultant of two forces each of a unit magnitude,acting at a point ,is of unit magnitude, then angle between these forces, is

  • A \({ 45 }^{ \circ }\)
  • B \({ 60 }^{ \circ }\)
  • C \({ 90 }^{ \circ }\)
  • D \({ 120 }^{ \circ }\)
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