Mathematics In Physics Test

Result

Mathematics In Physics Test - 22

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Weekly Quiz Competition

Question 1
1 / -0

A
are perpendicular to each other

B
act in the same direction

C
act in the opposite direction

D
can act in any direction

Solution
Question 2
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The dot product of two mutual perpendicular vector is:

A
0

B
1

C
∞

D
None of the above

Solution
Question 3
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Current in a circuit is given by i = 3t²+ 2t. Find charge that crosses a cross-section from time t=0 to t=2 sec.

A
12 C

B
10 C

C
8 C

D
2 C

Solution
Question 4
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Let θ be the angle between vectors Which of the following figures correctly represents the angle θ?

A

B

C

D

Solution

Hint: Take angle between the tails or the heads

The angle between the two vectors is always taken between head to head or tail to tail and it must be acute.
Question 5
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If the angle between the two forces increases, the magnitude of their resultant:

A
Decreases

B
Increases

C
Remains unchanged

D
First decreases, then increases

Solution

The angle between two vectors can never be greater than 180^o.

So, on increasing the θ, the magnitude of resultant vectors decreases.
Question 6
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The vector sum of two forces is perpendicular to their vector difference. In that case, the forces:

A
are not equal to each other in magnitude.

B
cannot be predicted.

C
are equal to each other.

D
are equal to each other in magnitude.

Solution
Question 7
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Which one of the following statements is true?

A
a scalar quantity is the one that is conserved in a process.

B
a scalar quantity is the one that can never take negative values.

C
a scalar quantity is the one that does not vary from one point to another in space.

D
a scalar quantity has the same value for observers with different orientations of the axes.

Solution

Hint: Recall the definition of scalar and vector quantities.

A scalar quantity is independent of direction hence has the same value for observers with different orientations of the axes.
Question 8
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Figure shows the orientation of two vectors u and v in the XY plane.

which of the following is correct?

A
a and p are positive while b and q are negative

B
a, p, and b are positive while q is negative

C
a, q, and b are positive while p is negative

D
a, b, p, and q are all positive

Solution

(b) Hint: We can resolve the vectors along the coordinate axises.

Step 1: Find the direction of u.

Clearly from the diagram,

As u is in the first quadrant, hence both components a and b will be positive.

Step 2: Find the direction of v.

For . as it is in positive x-direction and located downward hence x-Component p will be positive and y-component q will be negative.
Question 9
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The component of a vector r along x-axis will have maximum value if:

A
r is along positive y-axis

B
r is along positive x-axis

C
r makes an angle of 45^∘ with the x-axis

D
r is along negative y-axis

Solution

The component should be at an angle of 0^∘ from the axis given here and thus the component of the vector along x-axis will have the maximum value when r is along x-axis.
Question 10
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Consider the quantities, pressure, power, energy, impulse, gravitational potential, electrical charge, temperature, area. Out of these, the only vector quantities are

A
Impulse, pressure and area

B
Impulse and area

C
Area and gravitational potential

D
Impulse and pressure

Solution

We know that impulse J = F.Δt = Δp, where F is force, At is time duration and Ap is change in momentum. As Δp is a vector quantity, hence impulse is also a vector quantity. Sometimes area can also be treated as vector direction of area vector is perpendicular to its plane.