Mathematics In Physics Test

Result

Mathematics In Physics Test - 4

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Question 1
1 / -0

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

A
0⁰

B
90⁰

C
45⁰

D
180⁰

Solution
Question 2
1 / -0

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

A
90°

B
45°

C
180°

D
0°

Solution

Suppose two vectors are P and Q. It is given that: |P+Q| = |P−Q|

Let the angle between P and Q is θ.

⇒ P²+ Q²+ 2PQcosθ = P²+Q²− 2PQcosθ

⇒ cosθ = 0 = cos90⁰

⇒ θ = 90⁰
Question 3
1 / -0

If vectors A = cosωt + sinωt and B = (cosωt/2) + (sinωt/2) are functions of time, then the value of t at which they are orthogonal to each other

A
t = π/4ω

B
t = π/2ω

C
t = π/ω

D
t = 0

Solution

For perpendicular vector we have A.B=0

=>cosωt cosωt/2 + sinωt sinωt/2=0

[∴cos(A-B)=cosA.cosB+ sinA.sinB]

=>cos(ωt-ωt/2)=0

cosωt/2=0

=> ωt/2=π/2

=> t=π/ω

Thus, time taken by vectors which are orthogonal to each other is π/ω
Question 4
1 / -0

Six vectors have the directions as indicated in the figure. Which of the following statements may be true?

A

B

C

D

Solution

If two non-zero vectors are represented by the two adjust sides of a parallelogram, then the resultant is given by the diagonal of the parallelogram passing through the point of intersection of the two vectors
Question 5
1 / -0

A particle moves from a point when a force of is applied. How much work has been done by the force?

A
8 J

B
11 J

C
5 J

D
2 J

Solution
Question 6
1 / -0

In the given figure

A

B

C

D

Solution

The angle between vectors is the angle between tails/heads.
Question 7
1 / -0

A force of 6 N and another of 8 N can be applied together to produce the effect of a single force of -

A
1 N

B
11 N

C
15 N

D
20 N

Solution
Question 8
1 / -0

Which of the sets given below may represent the magnitude of resultant of three vectors adding to zero?

A
2, 4, 8

B
4, 8, 16

C
1, 2, 1

D
0.5, 1, 2

Solution
Question 9
1 / -0

A blind person after walking 10 steps in one direction, each of length 80 cm, turns randomly to the left or to the right by 90°. After walking a total of 40 steps the maximum possible displacement of the person from his starting position could be -

A
320 m

B
32 m

C
16/√2 m

D
16√2 m

Solution

Possible case of max. displacement

If a person starts from A and reaches B,

= 16√2 m
Question 10
1 / -0

The resultant of two vectors A and B is perpendicular to the vector A and its magnitude is equal to half the magnitude of vector B. The angle between A and B is -

A
120°

B
150°

C
135°

D
None of these

Solution

Angle between A & B= 180°−θ

= 180° − 30°

= 150°