Vector Addition

Q. If the magnitude of the resultant of two vectors of equal magnitudes is equal to the magnitude of either vectors, then the angle between two vectors is

1. ${125}^o$
2. ${130}^o$
3. ${110}^o$
4. ${120}^o$

Q. A person moves $30\text{m}$ north and then $20\text{m}$ towards east and finally $30\sqrt{2}\text{m}$ in south-west direction. Displacement of the person from the origin will be

1. $10m$ along north
2. $10m$ along west
3. Zero
4. $10m$ along south

Q. Explain the triangle law of vector addition.

Q. The resultant of the two vectors makes angles ${30}^{\circ }$ and ${60}^{\circ }$ with them and the magnitude of the resultant is $40$. The magnitudes of two vectors are

1. $20$ and $40$
2. $20$ and $25$
3. $20$ and $20\sqrt{3}$
4. $10\sqrt{3}$ and $20$

Q. Three forces acting on a body are shown in the figure. To have the resultant force only along the y-direction, the magnitude of the minimum additional force needed is

1. $\sqrt{3}N$
2. $\frac{\sqrt{3}}{4}N$
3. $0.5N$
4. $1.5N$

Q. The resultant of two forces, one double the other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces is

1. ${60}^{\circ }$
2. ${120}^{\circ }$
3. ${150}^{\circ }$
4. ${90}^{\circ }$

Q. The vector sum of the forces $10N$ and $6N$ can be

1. $2N$
2. $18N$
3. $8N$
4. $20N$

Q. A motorboat is racing towards north at $25\text{km/h}$ and the water current in that region is $10\text{km/h}$ in the direction of ${60}^{\circ }$ east of south. The resultant velocity of the boat is

1. $22\text{km/hr}$, at an angle ${\tan }^{-1}\left(0.343\right)$ North of East.
2. $22\text{km/hr}$, at an angle ${\tan }^{-1}\left(0.433\right)$ East of North.
3. $20\text{km/hr}$, at an angle ${\tan }^{-1}\left(0.433\right)$ East of North.
4. $20\text{km/hr}$, at an angle ${\tan }^{-1}\left(0.343\right)$ North of East.

Q.

A spring of force constant k is cut into two pieces such that one piece is double the length of the other. Then the long piece will have a force constant of____

Q.

If the volume of a parallelopiped, whose coterminous edges are given by the vectors $a=i+j+nk,b=2i+4j-nk,$ and $c=i+nj+3k;\left(n\ge 0\right)$, is $158$ cubic units, then:

1. $a·c=17$

2. $b·c=10$

3. $n=9$

4. $n=7$

Q. a=vdv/DX how?

Q. Rain is falling vertically with a speed of $35\text{m/s}$. Wind starts blowing after some time with a speed of $12\text{m/s}$ from east to west direction. For a boy waiting at a bus stop, the velocity of the rain appears to be

1. $35\text{m/s}$ at an angle of ${\tan }^{-1}\left(0.343\right)$ with the vertical.
2. $37\text{m/s}$ at an angle of ${\tan }^{-1}\left(2.92\right)$ with the vertical.
3. $35\text{m/s}$ at an angle of ${\tan }^{-1}\left(2.92\right)$ with the vertical.
4. $37\text{m/s}$ at an angle of ${\tan }^{-1}\left(0.343\right)$ with the vertical.

Q. The minimum number of vectors of unequal magnitudes required to produce a zero resultant is

1. 3
2. 4
3. More than 4
4. 2

Q. If $|\overrightarrow{A}+\overrightarrow{B}|=|\overrightarrow{A}|+|vecB$, then angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ will be

1. ${60}^{\circ }$
2. ${90}^{\circ }$
3. ${120}^{\circ }$
   
4. $0^{\circ }$
   

Q. A particle moving with a velocity $\overrightarrow{V}$ is acted by three forces as shown by the vector triangle PQR. The velocity of the particle will

1. increase
2. decrease
3. change according to the smallest force $\overrightarrow{QR}$
4. remains constant

Q.

A carrom board (4 ft $\times$ 4 ft square) has the queen at the centre. The queen, hit by the striker moves to the front edge, rebounds and goes in the hole behind the striking line. Find the magnitude of displacement of the queen

(a) from the centre to the front edge,

(b) from the front edge to the hole and (c) from the centre to the hole.

Q. The resultant of two vectors $\overrightarrow{P}$ and $\overrightarrow{Q}$ is $\overrightarrow{R}$. If magnitude of $\overrightarrow{Q}$ is doubled, the new resultant is perpendicular to $\overrightarrow{P}.$ Then $|\overrightarrow{R}|$ equals

1. $|\overrightarrow{P}|$
2. $|(\overrightarrow{P}+\overrightarrow{Q})|$
3. $|\overrightarrow{Q}|$
4. $|\overrightarrow{P}-\overrightarrow{Q}|$

Q.

If vectors P, Q and R have magnitude 5, 12 and 13 units and $\overrightarrow{P}+\overrightarrow{Q}=\overrightarrow{R}$, the angle between Q and R is

1. $co{s}^{-1}\frac{7}{13}$

2. $co{s}^{-1}\frac{5}{12}$
   

3. $co{s}^{-1}\frac{12}{13}$
   

4. $co{s}^{-1}\frac{5}{13}$
   

Q.

find the magnitude of two forces such that if they are at right angles their resultant is root 10 Newton what is there at 60 degree their resultant is root 13 Newton

Q.

Find the resultant of 2 vectors whose magnitude is 6 and 8 and make an angle of 90 degrees between them.

1. 12

2. 10

3. 6

4. 8

Q.

State and prove parallelogram law of vector addition

Q.

A particle in SHM is described by the displacement

equation x(t) = A cos ( $\omega t+\theta )$ . If the initial (t = 0)

position of the particle is 1 cm and its initial

velocity is $\pi$ cm/s, what is its amplitude?

The angular frequency of the particle is $\pi s^{-1}$

1. 2.5 cm

2. 1 cm

3. 2 cm

4. 

Q.

What is the use of arithmetic progression in daily life?

Q. If the angle between two forces increases, the magnitude of their resultant

1. decreases
2. remains unchanged
3. increases
4. first decreases and then increases

Q. The sum of the measures of the angles of regular polygen is ${2160}^{\circ }$. How many sides does it have ?

1. $16$
2. $18$
3. $14$
4. $12$

Q.

Can resultant of three vectors be zero?

Q.

A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/sec. A plumb bob is suspended from the roof of the car by a light rigid rod of length 1.00 m. The angle made by the rod with the vertical is

1. Zero

2. 

3. 

4. 

Q.

How to find resultant of two vectors?

Q. A block of mass $m$, is kept on a wedge of mass $M$, as shown in figure such that mass $m$ remains stationary w.r.t wedge. The magnitude of force $P$ is

1. $g\tan \beta$
2. $mg\tan \beta$
3. $(m+M)g\tan \beta$
4. $mg\cot \beta$

Q. Four particles, each of mass $M$, move along a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each particle is
(Assume that each particle is diameterically opposite to other in pair.)

1. $\frac{GM}{R}$
2. $\sqrt{2\sqrt{2}\frac{GM}{R}}$
3. $\sqrt{\frac{GM}{R}(2\sqrt{2}+1)}$
4. $$\sqrt{\frac{GM}{R}(\frac{2\sqrt{2}+1}{4})}$$