### 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 ${ 120 }^{ \circ }$