Motion in A Plane Online Objective Test | Motion in A Plane Online Objective Test

# Motion in A Plane # CBSE 11TH PHYSICS Prepare / Learn

Q1. We can define the difference of two vectors A and B as the

A. sum of two vectors A and B' such that B' is equal to B multiplied by -1

B. sum of two vectors A and B' such that B' is equal to B multiplied by -2

C. sum of two vectors A and B' such that B' is equal to B multiplied by 1

D. sum of two vectors A and B' such that B' is equal to B multiplied by 0

Answer : Option A
Explaination / Solution:

Vector subtraction is defined in the following way.

The difference of two vectors, A - B , is a vector C that is, C = A - B
The addition of two vector such that C = A + (-B). B has been taken in opposite direction.

Thus vector subtraction can be represented as a vector addition.

# Motion in A Plane # CBSE 11TH PHYSICS Prepare / Learn

Q2. An arbitrary vector v can be expressed as

A. a sum of three mutually perpendicular unit vectors each multiplied by the same scalar constant

B. a sum of three mutually perpendicular unit vectors each multiplied by a some scalar constant

C. a sum of three mutually perpendicular unit vectors each multiplied scalar constant equal to 1

D. a sum of three mutually perpendicular unit vectors each multiplied scalar constant equal to -1

Answer : Option B
Explaination / Solution:

Set of elements (vectors) in a vector space is called a basis, or a set of basis vectors, if the vectors are linearly independent and every vector in the vector space is a linear combination of this set.In more general terms, a basis is a linearly independent spanning set.

Given a basis of a vector space, every element of vector space can be expressed uniquely as a linear combination of basis vectors, whose coefficients are referred to as vector coordinates or components.

We can represent vector v as

$\vec{v} = x \hat{i} + y \hat{j} + z \hat{k}$

# Motion in A Plane # CBSE 11TH PHYSICS Prepare / Learn

Q3. A unit vector is a vector

A. having a magnitude of 1 and points in z-direction

B. having a magnitude of 1 and points in x-direction

C. having a magnitude of 1 and points in y-direction

D. having a magnitude of 1 and points in any chosen direction

Answer : Option D
Explaination / Solution:

A unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat": $\hat{i}$ (pronounced "i-hat"). The term direction vector is used to describe a unit vector being used to represent spatial direction.

$\hat{i} =$ a unit vector directed along the positive x axis

$\hat{j}$ = a unit vector directed along the positive y axis

$\hat{k}$ = a unit vector directed along the positive z axis

# Motion in A Plane # CBSE 11TH PHYSICS Prepare / Learn

Q4.

An arbitrary vector $\vec{A}$ in a plane can be expressed in terms of its x and y components by the equation

A. A⃗ =Axi^+Ayj

\vec{A} = A_{x} + A_{y}

\vec{A} = A_{x} \hat{i} - A_{y} \hat{j}

C. A⃗ =Axi^−Ayj

D. A⃗ =Ax−Ay

Answer : Option A
Explaination / Solution:

In a two-dimensional coordinate system, any vector can be broken into x -component and y -component.

Vector $\vec{A}$ can be represented as

$\vec{A} = A_{x} \hat{i} + A_{y} \hat{j}$

Where $A_{x}$ is component in direction of x-axis and $\hat{i}$ is a unit vector in same direction of x-axis

And $A_{y}$ is component in direction of y-axis and $\hat{j}$ is a unit vector in same direction of y-axis

# Motion in A Plane # CBSE 11TH PHYSICS Prepare / Learn

Q5.

If $A_{x}, A_{y} a n d B_{x}, B_{y}$ are components of vectors A and B along the x and y axis then the sum of the vectors A and B has a component in the x direction equal to

A_{x} - B_{x}

Ax−Bx

Ax+Bx

C. −Ax+Bx

D. −Ax−Bx

Answer : Option B
Explaination / Solution:

The component method of addition can be summarized this way:

Using trigonometry, find the x-component and the y-component for each vector.
Add up both x-components, (one from each vector), to get the x-component of the total.
Add up both y-components, (one from each vector), to get the y-component of the total.
Add the x-component of the total to the y-component of the total, and then use the Pythagorean theorem and trigonometry to get the size and direction of the total.

Using these points in mind, the sum of the vectors A and B has a component in the x direction $= A_{x} + B_{x}$

# Motion in A Plane # CBSE 11TH PHYSICS Prepare / Learn

Q6. if particles A and B are moving with velocities

v_{A}

and

v_{B}

(each with respect to some common frame of reference, say ground.). Then, velocity of particle A relative to that of B is:

v_{A B}

v_{A}

v_{B}

v_{A B}

v_{A}

v_{B}

v_{A B}

= -

v_{A}

v_{B}

v_{A B}

= -

v_{A}

v_{B}

Answer : Option B
Explaination / Solution:

The relative velocity of an object A with respect to another object B is the velocity that object A would appear to have to an observer situated on object B moving along with it.

In simple words relative velocity of A with respect to Be is the vector difference between the velocities of A and B.

It is represented as

$V_{A B} = V_{A} - V_{B}$

# Motion in A Plane # CBSE 11TH PHYSICS Prepare / Learn

Q7. The path of a projectile is

A. straight line

B. cubic

C. hyperbola

D. a parabola

Answer : Option D
Explaination / Solution:

A particle with a vertical and horizontal velocity travelling in a gravitational field will trace out a parabola.

# Motion in A Plane # CBSE 11TH PHYSICS Prepare / Learn

Q8. Centripetal acceleration of a particle moving in a circular path with constant velocity v is given by

2 v^{2} / R

where R is the radius of the circle

2 v^{2} R

where R is the radius of the circle

v^{2} \times R

where R is the radius of the circle

v^{2} \times R

where R is the radius of the circle

Answer : Option D
Explaination / Solution:

A body that moves in a circular motion (of radius R) at constant speed (v) is always being accelerated. The acceleration is at right angles to the direction of motion (towards the center of the circle) and of magnitude

\frac{v^{2}}{R}

# Motion in A Plane # CBSE 11TH PHYSICS Prepare / Learn

Q9. Which of the following physical quantities a vector?

A. mass

B. angular momentum

C. speed

D. volume

Answer : Option B
Explaination / Solution:

Angular momentum is a vector quantity (more precisely, a pseudovector) that represents the product of a body's rotational inertia and rotational velocity about a particular axis.

# Motion in A Plane # CBSE 11TH PHYSICS Prepare / Learn

Q10. Which of the following physical quantities a scalar?

A. velocity

B. force

C. electric field

D. work

Answer : Option D
Explaination / Solution:

Work is defined as a dot-product (or scalar product) of force and displacement, both of which are vectors. A scalar (dot) product of two vectors gives a scalar result.

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