Zero Vector

Q. How many minimum number of coplanar vectors having different magnitudes can be added to give zero resultant

1. 3
2. 5
3. 4
4. 2

Q.

Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ lie in a plane, another vector $\overrightarrow{C}$ lies outside this plane, then the resultant of these three vectors i.e., $\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}$

1. Lies in the plane containing $\overrightarrow{A}+\overrightarrow{B}$

2. Lies in the plane containing $\overrightarrow{C}$

3. Can be zero

4. Cannot be zero

Q. A metal sphere is hung by a string fixed to a wall. The sphere is pushed away from the wall by a stick. The forces acting on the sphere are shown in the second diagram. Which of the following statements is wrong

1. none of these
2. P = W tan $\theta$
3. T= P+W
4. $T^2$ = $P^2$ + $W^2$

Q. Which of the following is a null vector?

1. Velocity vector of a body moving in a circle with a uniform speed
2. Velocity vector of a body moving in a straight line with a uniform speed
3. Position vector of the origin of a rectangular coordinate system
4. Displacement vector of a stationary object
   

Q.

Q. resultant of which of the following may be equal to zero

a) 10N , 10N, 10N

b)10N, 10N, 25N

c)10N, 10N, 35N

Q.

Can you have a negative vector?

Q.

What is the difference between null vector and zero vector?

Q. A null vector has

1. zero magnitude and a specific direction
2. a finite magnitude and no specific direction
3. a finite magnitude and a specific direction
4. zero magnitude and no specific direction

Q. 100 coplanar forces each equal to 10 N act on a body. Each force makes angle $\frac{\pi }{50}$ with the preceding force. What is the resultant of the forces

1. 250 N
2. Zero
3. 1000 N
4. 500 N

Q. How many minimum number of coplanar vectors having different magnitudes can be added to give zero resultant

1. 2
2. 3
3. 4
4. 5

Q.

A horizontal force $F$ is applied to a small object $P$ of mass $m$ on a smooth plane inclined to the horizon at an angle $\theta$. If $F$ is just enough to keep $P$ in equilibrium, then $F=$?

1. $mg{\cos }^2\theta$

2. $mg{\sin }^2\theta$

3. $mg\cos \theta$

4. $mg\tan \theta$

Q. If multiple vectors cancel out then what do we get ?

1. 0
2. 0 vector
3. \N
4. \N

Q. $100$ coplanar forces each equal to $10$ N act on a body. Each force makes angle $\pi /50$ with the preceding force. What is the resultant of the forces.

1. $1000$ N
2. $500$ N
3. $250$ N
4. Zero

Q. Three forces $F_1=2\overline{i}+\overline{j}-\overline{k}N,F_2=2\overline{i}+3\overline{j}-3\overline{k}$ N, $F_3=a(\overline{i}+\overline{j}-\overline{k})$ N act simultaneously on a particle. The value of ${}^{\prime }{a}^{\prime }$ so that the particle may be in equilibrium is:

1. 4
2. -4
3. 2
4. 6

Q. The force acting on a body moving along x-axis varies with the position of the particle as shown in the figure. The body is in stable equilibrium at

1. $x=x_1$
2. $x=x_2$
3. both $x_1$ and $x_2$
4. neither $x_1$ nor $x_2$

Q. Three forces $\overrightarrow{F_1}=(3\hat{i}+2\hat{j}-\hat{k})N,\overrightarrow{F_2}=(3\hat{i}+4\hat{j}-5\hat{k})N$ and $\overrightarrow{F_3}=A(\hat{i}+\hat{j}-\hat{k})N$ act simultaneously on a particle. In order that the particle remains in equilibrium, the value of A should be

1. -6
2. 6
3. 9
4. -9

Q. Three forces $\overrightarrow{F_1}=(3\hat{i}+2\hat{j}-\hat{k})N,\overrightarrow{F_2}=(3\hat{i}+4\hat{j}-5\hat{k})N$ and $\overrightarrow{F_3}=A(\hat{i}+\hat{j}-\hat{k})N$ act simultaneously on a particle. In order that the particle remains in equilibrium, the value of A should be

1. -6
2. 6
3. 9
4. -9

Q. A pendulum is hanging from the ceiling of a car having an acceleration $a_0$ with respect to the road. find the angle made by the string with the vertical.

Q. Direction of zero vector is

1. Towards origin
2. Indeterminate
3. Away from the origin
4. Towards $x-$axis

Q.

how to calculate magnitude?

Q. A null vector has

1. zero magnitude and a specific direction
2. a finite magnitude and no specific direction
3. a finite magnitude and a specific direction
4. zero magnitude and no specific direction

Q. 100 coplanar forces each equal to 10 N act on a body. Each force makes angle $\frac{\pi }{50}$ with the preceding force. What is the resultant of the forces

1. 1000 N
2. 500 N
3. 250 N
4. Zero

Q. Direction of zero vector

1. does not exist
2. towards origin
3. indeterminate
4. None of these

Q. Five coplanar forces of equal magnitudes $10N$ each, act at a point such that the angle between any two consecutive forces is same. The magnitude of their resultant is :

1. $10N$
2. $0$
3. $20N$
4. $10\sqrt{2}N$

Q. zero vector = * vector

1. Zero
2. Zero vector
3. None of these

Q. If $F=2x^2-3x-2$, then select the correct statement.

1. $x=-\frac{1}{2}$ is the position of stable equilibrium
2. $x=2$ is the position of stable equilibrium
3. $x=-\frac{1}{2}$ is the position of unstable equilibrium
4. $x=2$ is the position of neutral equilibrium

Q. Two forces A and B act on an object in opposite directions. A is bigger than B. The net force on the object is

1. $A+B$ acting in the direction of A.
2. $A-B$ acting in the direction of A.
3. $A+B$ acting in the direction of B.
4. $A-B$ acting in the direction of B.

Q.

Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ lie in a plane, another vector $\overrightarrow{C}$ lies outside this plane, then the resultant of these three vectors i.e., $\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}$

1. Can be zero

2. Cannot be zero

3. Lies in the plane containing $\overrightarrow{A}+\overrightarrow{B}$

4. Lies in the plane containing $\overrightarrow{C}$

Q. A particle experiences a position-dependent force given by
$F\left(x\right)=-6x^2+4x+3/x^2$
where $x$ is in meters and $F$ is in Newtons (units have been abbreviated).
At $x=1m$, what is the potential energy of the particle relative to the potential energy at the origin?

1. $+5J$
2. Cannot be determined
3. $-3J$
4. $+3J$
5. $-5J$

Q. Two equal forces $\overrightarrow{F}$ each act at right angles to each other.The third force which can neutralize their effect is:

1. $2F$, in the same plane of the two forces
2. $\sqrt{2}F$, in the same plane of the two forces
3. $\sqrt{2}F$, in the different plane of the two forces.
4. $2F$, in the different plane of the two forces.