Mathematics In Physics Test

Result

Mathematics In Physics Test - 11

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Question 1
1 / -0

The resultant force acting on particle is:

A

B

C

D

Solution
Question 2
1 / -0

A= 4i + 4j − 4k and B = 3i + j + 4k, then angle between vectors A and B is:

A
180°

B
90°

C
45°

D
0°

Solution

The angle between two vector will be given by-
Question 3
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If vectors and are functions of time. Then, at what value of t are they orthogonal to one another?

A

B

C

D
t = 0

Solution

Hint: The dot product of two orthogonal vectors is equal to zero.

Step 1: Find the dot product of two vectors.
Question 4
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Six vectors through have the magnitudes and directions indicated in the figure. Which of the following statements is true?

A

B

C

D

Solution

Hint: Use the triangle law of addition of vectors.

Step 1: Add any two vectors and find the resultant.

In the given figure the vectors can be joined to make two adjacent 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.

Step 2: Find any three vectors that follow the parallelogram method or triangle law of addition.
Question 5
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are two vectors and θ is the angle between them.

If

then the value of θ will be:

A
60^o

B
45^o

C
30^o

D
90^o

Solution

Hint: Use the formulae of dot product and the cross product.
Question 6
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If a curve is governed by the equation y=sinx, then the area enclosed by the curve and x-axis between x =0 and x = π is (shaded region) :

A
1 unit

B
2 units

C
3 units

D
4 units

Solution
Question 7
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The acceleration of a particle starting from rest varies with time according to relation, a = α t + β. The velocity of the particle at time instant t is: (Here, a = dv/dt)

A
αt² + βt

B
αt² + βt/2

C
αt²/2 + βt

D
2αt² + βt

Solution
Question 8
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The displacement of the particle is zero at t=0 and at t=t it is x. It starts moving in the x-direction with a velocity that varies as v = k√x, where k is constant. The velocity will :

(Here, v = dx/dt)

A
vary with time.

B
be independent of time.

C
be inversely proportional to time.

D
be inversely proportional to acceleration.

Solution

Thus velocity varies with time.
Question 9
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The acceleration of a particle is given as a = 3x². At t = 0, v = 0 and x = 0. It can then be concluded that the velocity at t = 2 sec will be:

A
0.05 m/s

B
0.5 m/s

C
5 m/s

D
50 m/s

Solution
Question 10
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The acceleration of a particle is given by a=3t at t=0, v=0, x=0. The velocity and displacement at t = 2 sec will be:

A
6 m/s, 4 m

B
4 m/s, 6 m

C
3 m/s, 2 m

D
2 m/s, 3 m

Solution