Laws of Motion Test

Result

Laws of Motion Test - 3

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Question 1
1 / -0

If you calculate the cross product A × B and B × A, how will the result compare?

A
They will be exactly the same.

B
They will have the same magnitude, but different directions.

C
They will have different magnitudes, but the same direction.

D
They will have different magnitudes and directions.

Solution

The magnitude of the cross product A and B is determined using the formula,

A × B = A B sin θ

Where θ is the angle between the two vectors A and B

A and B are the magnitudes of the vector.

Now, the direction of the cross product of the vectors is given by the right hand rule,

The right-hand rule states that the orientation of the vectors' cross product is determined by placing the right hand, extending it in the direction of A, and then curling the fingers in the direction that the angle A makes with B. The thumb then points in the direction of A × B.

In case of A × B, the thumb points toward the outward direction. On the other hand, the direction of the cross product B × A will be inward to the plane of the two vectors.
Question 2
1 / -0

Let F be a force acting on a particle having position vector r. Let τ be the torque of this force about the

origin, then

A
r . τ = 0 and F. τ = 0

B
r . τ = 0 but F. τ ≠ 0

C
r . τ ≠ 0 but F. τ = 0

D
r . τ ≠ 0 and F. τ ≠ 0

Solution

We have torque, τ = r × F

The torque is perpendicular to both the vectors r and F. Thus the dot product of τ with r and F will be zero.

Since the dot product between a . b = a b cos θ

θ is 90° therefore, the dot product will be zero.
Question 3
1 / -0

Read the two statements provided below and then pick the correct option.

Statement 1: If ice caps of the pole melt, the day length will shorten

Statement 2: Ice flows towards the equator and decreases the moment of inertia of the earth and hence increases the frequency of rotation of the earth.

A
Both statement 1 and 2 are true and statement2 is the correct explanation of statement 1

B
Both statement 1 and 2 are true but statement 2 is not the correct explanation of statement 1

C
Statement 1 is true but statement 2 is false

D
Statement 1 and 2 are false

Solution

Both the assertion made in statement 1 and the reason in the second statement is incorrect. If the ice caps of the pole melt, the water will flow towards the equator and the moment of inertia increases. In order to conserve the angular momentum of the earth, the frequency of rotation decreases in turn increases the time span of one day.