EASY

Earn 100

A vector in $x - y$ plane makes an angle of $30^{o}$ with $y$ -axis. The magnitude of $y$ -component of vector is $2 \sqrt{3}$ . The magnitude of $x$ -component of the vector will be :

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Important Questions on Kinematics

EASY

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

Vector

\vec{a} = \hat{i} + 2 \hat{j} + 2 \hat{k}

and

\vec{b} = \hat{i} - \hat{j} + \hat{k}

. What is the unit vector along

\vec{a} + \vec{b}

MEDIUM

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

Two forces

P

and

Q

, of magnitude

2 F

and

3 F

, respectively, are at an angle

θ

with each other. If the force

Q

is doubled, then their resultant also gets doubled. Then, the angle

θ

is:

EASY

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

Force

\vec{F}

applied on a body is written as

\vec{F} = (\hat{n} \times \vec{F}) \cdot \hat{n} + \vec{G}

, where

\hat{n}

is a unit vector. The vector

\vec{G}

is equal to

EASY

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

\vec{A} = 3 \hat{i} - 2 \hat{j} + \hat{k}, \vec{B} = \hat{i} - 3 \hat{ȷ} + 5 \hat{k}

and

\vec{C} = 2 \hat{i} + \hat{j} - 4 \hat{k}

form a right angled triangle then out of the following which one is satisfied?

EASY

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

One of the rectangular components of a force of

40 N

20 \sqrt{3} N

. What is the other rectangular component?

EASY

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

Figure shows three forces ${\vec{F}}_{1}, {\vec{F}}_{2}$ and ${\vec{F}}_{3}$ acting along the sides of an equilateral triangle. If the total torque acting at point $O$ (centre of the triangle) is zero then the magnitude of ${\vec{F}}_{3}$ is

Question Image

MEDIUM

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

A vector

\vec{A}

is rotated by a small angle

∆ θ

radians

(∆ θ ≪ 1)

to get a new vector

\vec{B}

. In that case

|\vec{B} - \vec{A}|

is :

MEDIUM

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

The unit vector perpendicular to the plane of

\vec{A} = \hat{i} - 3 \hat{j} - \hat{k}

and

\vec{B} = 2 \hat{i} + \hat{j} - \vec{k}

EASY

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

The angle made by

\vec{r} = 3 \hat{i} + 3 \hat{j}

with the

x

axis is

EASY

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

If y-component of a force acting in x-y plane is $2 \sqrt{3} N$ . Then the x- component will be

Question Image

EASY

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

The unit vector

(a \hat{i} + b \hat{j})

is perpendicular to

(\hat{i} + \hat{j}) .

The value of

b

can be:

MEDIUM

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

Consider a frame that is made up of two thin massless rods $A B$ and $A C$ as shown in the figure. A vertical force $\vec{P}$ of magnitude $100 N$ is applied at point $A$ of the frame.

Question Image

Suppose the force is $\vec{P}$ resolved parallel to the arms $A B$ and $A C$ of the frame. The magnitude of the resolved component along the arm $A C$ is $x N$ . The value of $x$ , to the nearest integer, is ________.

[Given : $\sin (35 °) = 0.573, \cos (35 °) = 0.819, \sin (110 °) = 0.939, \cos (110 °) = - 0.342$ ]

EASY

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

Vector

A

has a magnitude of

10

units and makes an angle of

30 °

with the positive x-axis. Vector

B

has a magnitude of

20

units and makes an angle of

30 °

with the negative x-axis. What is the magnitude of the resultant between these two vectors?

MEDIUM

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

Resultant of two vectors

\vec{P}

and

\vec{Q}

is of magnitude

R_{1} .

If direction of

\vec{Q}

is reversed, the resultant is of magnitude

R_{2}

. The value of

(R_{1}^{2} + R_{2}^{2})

[\cos (π - θ) = - \cos θ]

HARD

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

In an octagon $A B C D E F G H$ of equal side, what is the sum of $\vec{A B} + \vec{A C} + \vec{A D} + \vec{A E} + \vec{A F} + \vec{A G} + \vec{A H},$ if, $\vec{AO} = 2 \hat{i} + 3 \hat{j} - 4 \hat{k}$

Question Image

EASY

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

Two vectors

\vec{P}

and

\vec{Q}

have equal magnitudes. If the magnitude of

\vec{P} + \vec{Q}

n

times the magnitude of

\vec{P} - \vec{Q},

then angle between

\vec{P}

and

\vec{Q}

EASY

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

The angle between two vectors

x

and

y

θ

. If the resultant vector

z

makes an angle

\frac{θ}{2}

with

x

, then which of the following is true?

MEDIUM

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

Two vectors

\vec{A}

and

\vec{B}

have equal magnitudes. The magnitude of

(\vec{A} + \vec{B})

n

times the magnitude of

(\vec{A} - \vec{B})

. The angle between

\vec{A}

and

\vec{B}

is:

MEDIUM

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

The resultant of these forces $\vec{O P}, \vec{O Q}, \vec{O R}, \vec{O S}$ and $\vec{O T}$ is approximately ______ $N .$
[Take $\sqrt{3} = 1.7, \sqrt{2} = 1.4$ Given $\hat{i}$ and $\hat{j}$ unit vectors along $x, y$ axis]

Question Image

EASY

Physics>Mechanics>Kinematics>Basics of Motion in a Plane

\vec{A}

and

\vec{B}

are two non-zero vectors inclined at an angle

θ

\hat{a}

and

\hat{b}

are unit vectors along

\vec{A}

and

\vec{B}

respectively. The component of

\vec{A}

in the direction of

\vec{B}

A vector in x-y plane makes an angle of 30o with y-axis. The magnitude of y-component of vector is 23. The magnitude of x-component of the vector will be :

Important Questions on Kinematics

Learn and Prepare for any exam you want !

A vector in $x - y$ plane makes an angle of $30^{o}$ with $y$ -axis. The magnitude of $y$ -component of vector is $2 \sqrt{3}$ . The magnitude of $x$ -component of the vector will be :