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Question (1)

QN0034951

If vectors and are functions of time, then the value of at which they are orthogonal to each other is :

(A)
(B)
(C)
(D)

Correct Answer: B

Explanation:

Two vectors are

For two vectors and to be orthogonal

So,

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Question (2)

QN0034952

The position vector of a particle as a function of time is given by: ,Where is in meter, in seconds and and denote unit vectors along -and -directions, respectively. Which one of the following statements is wrong for the motion of particle? NCERT-81/N-42, AIPMTZ 2015 RS, C

(A)
Magnitude of acceleration vector is , where is the velocity of particle
(B)
Magnitude of the velocity of particle is 8 meter/ second
(C)
path of the particle is a circle of radius 4 meter.
(D)
Acceleration vector is along

Correct Answer: B

Explanation:

Here,

Squaring and adding equations (i) and (ii)

Motion of the particle is circular motion, acceleration vector is along and its magnitude

Velocity of particle,

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Question (3)

QN0034953

A ship is moving Westwards with a speed of and a ship B South of A, is moving Northwards with a speed of . The time after which the distance between them becomes shortest, is

(A)
(B)
(C)
(D)

Correct Answer: A

Explanation:

Distance

Time taken to reach the shortest distance between and

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Question (4)

QN0034954

A particle moves so that its position vector is given by . Where is a constant. Which of the following is true?

(A)
Velocity and acceleration both are perpendicular to
(B)
Velocity and acceleration both are parallel to
(C)
Velocity is perpendicular to and acceleration is directed towards the origin
(D)
Velocity is perpendicular to and acceleration is directed away from the origin

Correct Answer: C

Explanation:

Given: Position vector

Velocity,

and acceleration,

hence and

is directed towards the origin.

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Question (5)

QN0034955

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is :

(A)
(B)
(C)
(D)

Correct Answer: B

Explanation:

Squaring on both sides

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Question (6)

QN0034956

The and coordinates of the particle at any time are and respectively, where and are in meters and in seconds. The acceleration of the particle at is

(A)
(B)
(C)
(D)
0

Correct Answer: B

Explanation:

Given:

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Question (7)

QN0034957

The moment of the force, at , about the point , is given by

(A)
(B)
(C)
(D)

Correct Answer: C

Explanation:

Moment of force,

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Question (8)

QN0034958

When an object is shot from the bottom of a long smooth inclined plane kept at an angle with horizontal, it can travel a distance along the plane. But when the inclination is decreased to and the same object is shot with the same velocity, it can travel distance. Then will be:

(A)
(B)
(C)
(D)

Correct Answer: C

Explanation:

When object shot from inclined plane kept at and velocity say , then distance travel

When object shot from inclined plane kept at and same velocity , then distance travel

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Question (9)

QN0034959

A car starts from rest and accelerates at . At , a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at ? (Take

(A)
(B)
(C)
(D)

Correct Answer: A

Explanation:

Velocity of car at velocity the ball dropped out of a window at

Velocity of ball along the horizontal and is .

After 2 seconds of motion :

Vertical velocity of ball

Magnitude of velocity of ball

Since the ball is under free fall.

Acceleration of ball (a) at

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Question (10)

QN0034960

A particle moving in a circle of radius with a uniform speed takes a time to complete one revolution. If this particle were projected with the same speed at an angle ' ' to the horizontal, the maximum height attained by it equals . The angle of projection, , is then given by:

(A)
(B)
(C)
(D)

Correct Answer: A

Explanation:

Speed of particle to complete one revolution,

Particle is projected with same speed (U) at an angle q to the horizontal

Maximum Height

or, given

or,

(using equation (i))

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Question (1)

If vectors and are functions of time, then the value of at which they are orthogonal to each other is :

Explanation:

Link:

Question (2)

The position vector of a particle as a function of time is given by: ,Where is in meter, in seconds and and denote unit vectors along -and -directions, respectively. Which one of the following statements is wrong for the motion of particle? NCERT-81/N-42, AIPMTZ 2015 RS, C

Explanation:

Link:

Question (3)

A ship is moving Westwards with a speed of and a ship B South of A, is moving Northwards with a speed of . The time after which the distance between them becomes shortest, is

Explanation:

Link:

Question (4)

A particle moves so that its position vector is given by . Where is a constant. Which of the following is true?

Explanation:

Link:

Question (5)

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is :

Explanation:

Link:

Question (6)

The and coordinates of the particle at any time are and respectively, where and are in meters and in seconds. The acceleration of the particle at is

Explanation:

Link:

Question (7)

The moment of the force, at , about the point , is given by

Explanation:

Link:

Question (8)

When an object is shot from the bottom of a long smooth inclined plane kept at an angle with horizontal, it can travel a distance along the plane. But when the inclination is decreased to and the same object is shot with the same velocity, it can travel distance. Then will be:

Explanation:

Link:

Question (9)

A car starts from rest and accelerates at . At , a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at ? (Take

Explanation:

Link:

Question (10)

A particle moving in a circle of radius with a uniform speed takes a time to complete one revolution. If this particle were projected with the same speed at an angle ' ' to the horizontal, the maximum height attained by it equals . The angle of projection, , is then given by:

Explanation:

Link:

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