Question 1

Which of the following is the correct dimensional formula for pressure in the SI system?

Accepted Answer

$$[M][L]^{-1}[T]^{-2}$$

Question 2

Given the formula $$P = \sqrt{v^2$ \cdot D} + a$$, where $$P is $$pressure, $$v is $$velocity, $$D is $$density, and $$a is $$acceleration, which of the following statements is true regarding dimensional consistency?

Accepted Answer

Both $$\sqrt{v^2$ \cdot D}$$ and $$a$$ must have the same dimensions as $$P$$

Question 3

Which of the following is the correct dimensional formula for energy?

Accepted Answer

$$[M][L]^{2}[T]^{-2}$$

Question 4

If $$A$$ and $$B$$ are two physical quantities with dimensions $$[A] = [L]$$ and $$[B] = [T]^{-1}$$, what is the dimension of $$A/B$$?

Accepted Answer

$$[L][T]^{-1}$$

Question 5

Which of the following is a correct property of dimensional analysis?

Accepted Answer

$$[A^n] = [A]^n$$

Question 6

A formula for the area $$A of a $$rectangle is $$A = l \cdot w$$, where $$l is $$length and $$w is $$width. What is the dimensional formula for area?

Accepted Answer

$$[L]^{2}$$

Question 7

Which of the following is the correct SI unit and dimensional formula for electric current?

Accepted Answer

Ampere ($$A$$), $$[I]$$

Question 8

If a physical quantity is dimensionless, which of the following is true?

Accepted Answer

Its dimensional formula is $$[1]$$

Question 9

Which of the following correctly expresses the dimensional formula for force?

Accepted Answer

$$[M][L][T]^{-2}$$

Question 10

A vector $$A$$ has components $$A_x = 3$$ and $$A_y = 4. $$What is the magnitude of $$A$$?

Accepted Answer

$$5$$

Question 11

If two vectors $$A$$ and $$B$$ are perpendicular, what is the value of their dot product $$A \cdot B$$?

Accepted Answer

$$0$$

Question 12

Which of the following is the correct formula for the cross product magnitude of two vectors $$A$$ and $$B$$ separated by angle $$	heta$$?

Accepted Answer

$$|A||B|\sin	heta$$

Question 13

Given vectors $$A = 2\hat{i} + 3\hat{j}$$ and $$B = -1\hat{i} + 4\hat{j}$$, what is $$A \cdot B$$?

Accepted Answer

$$10$$

Question 14

If a vector $$A is $$expressed as $$A = A_x \hat{i} + A_y \hat{j} + A_z \hat{k}$$, which component represents the projection of $$A on $$the $$y-$$axis?

Accepted Answer

$$A_y$$

Question 15

Which of the following is true about the sum of two vectors $$A$$ and $$B$$?

Accepted Answer

The resultant vector $$R is $$given by $$R = A + B$$

Question 16

If $$A = 4\hat{i} + 3\hat{j}$$, what is the unit vector in the direction of $$A$$?

Accepted Answer

$$\frac{4}{5}\hat{i} + \frac{3}{5}\hat{j}$$

Question 17

Which of the following is a correct property of the cross product $$A 	imes B$$?

Accepted Answer

It results in a vector perpendicular to both $$A$$ and $$B$$

Question 18

If $$A = 2\hat{i} + 3\hat{j}$$ and $$B = 4\hat{i} + 5\hat{j}$$, what is $$A + B$$?

Accepted Answer

$$6\hat{i} + 8\hat{j}$$

Question 19

Which of the following is the correct dimensional formula for velocity?

Accepted Answer

$$[L][T]^{-1}$$

Dimensional Analysis and Vectors in Physics: Study Notes

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