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Questions and Answers

Which of the following pairs of physical quantities have the same dimensional formula?

Velocity and Acceleration
Momentum and Force
Work and Power
Pressure and Stress (correct)

What is the dimensional formula for Kinetic Energy, given that Kinetic Energy is calculated as $KE = \frac{1}{2}mv^2$, where m is mass and v is velocity?

$ML^2T^{-2}$ (correct)
$MLT^{-2}$
$MLT^{-1}$
$M^2LT^{-2}$

Which of the following physical quantities is dimensionless?

Force
Velocity
Work
Strain (correct)

Which of the following physical quantities has a unit but no dimension?

Plane angle (B) Signup and view all the answers

In the equation $P + \frac{a}{V^2} = \frac{b\theta}{V}$, where P is pressure, V is volume, and $\theta$ is temperature, what are the dimensions of 'a'?

$ML^5T^{-2}$ (A) Signup and view all the answers

The van der Waals equation of state is given by $(P + \frac{an^2}{V^2})(V - nb) = nRT$, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. What are the dimensions of 'b'?

$L^3$ (D) Signup and view all the answers

Given the equation $v = at + bx^2$, where v represents velocity, t represents time, and x represents displacement, determine the dimensions of 'b'.

$LT^{-3}$ (B) Signup and view all the answers

If the centripetal force is given by $F = \frac{mv^2}{r}$, and the percentage errors in the measurements of m, v, and r are 1%, 2%, and 3% respectively, what is the percentage error in the measurement of the force?

7% (A) Signup and view all the answers

What are the dimensions of the Van der Waals constant 'a' in the equation $(P + \frac{a}{V^2})(V - b) = nRT$, where P is pressure and V is volume?

$ML^5T^{-2}$ (D) Signup and view all the answers

In dimensional analysis, if the period of oscillation T of a simple pendulum is expressed as $T = k \cdot m^x \cdot l^y \cdot g^z$, where m is mass, l is length, and g is acceleration due to gravity, what are the values of y and z?

$y = \frac{1}{2}, z = -\frac{1}{2}$ (D) Signup and view all the answers

Which of the following sets of quantities have the same number of significant figures?

23.08, 23.80, 43.00 (C) Signup and view all the answers

A metal cube has a mass of 8.654 g and a volume of 3.24 cm³. What is the density of the metal, expressed with the correct number of significant figures?

2.67 g/cm³ (B) Signup and view all the answers

What is the sum of 25.32 g, 10.1 g, and 5.222 g, expressed to the appropriate number of significant figures?

40.6 g (A) Signup and view all the answers

Which formula correctly relates kinetic energy (E) to mass (m) and velocity (v)?

$E = \frac{1}{2}mv^2$ (D) Signup and view all the answers

What are the limitations of using dimensional analysis?

It cannot derive the exact form of relationships, including dimensionless constants. (A) Signup and view all the answers

What is the number of significant figures in the number 5.00 x $10^{-5}$?

3 (D) Signup and view all the answers

What change maximizes torque, given a fixed force application?

Maximizing the distance (r) from the axis of rotation. (D) Signup and view all the answers

A force of $2\hat{i} - 3\hat{j} + \hat{k}$ acts on an object with a position vector of $-\hat{i} + \hat{j} - 2\hat{k}$. What is the resulting torque about the origin?

$5\hat{i} + 3\hat{j} + \hat{k}$ (B) Signup and view all the answers

Angular momentum is the rotational analog of what?

Linear momentum (D) Signup and view all the answers

Which of the following equations correctly relates angular momentum (l) and linear momentum (p)?

$l = r \times p$ (C) Signup and view all the answers

The moment of linear momentum is referred to as what?

Angular momentum (B) Signup and view all the answers

Which equation correctly relates torque ($\tau$) and angular momentum (L)?

$\tau = dL/dt$ (C) Signup and view all the answers

A spinning skater pulls their arms inward, decreasing their moment of inertia. According to the relationship between torque and angular momentum, what happens to their angular velocity if no external torques are acting?

Their angular velocity increases. (A) Signup and view all the answers

The time rate of change of the angular momentum of a particle is equal to what?

The torque acting on it (A) Signup and view all the answers

What physical principle is demonstrated by the equation $\frac{d\vec{L}}{dt} = \vec{\tau}$?

The relationship between net torque and angular momentum change. (C) Signup and view all the answers

A disc rotates with constant angular momentum. If the net torque acting on it is zero, which of the following quantities must remain constant?

The product of moment of inertia and angular velocity. (D) Signup and view all the answers

Flashcards

Fundamental (Base) Quantities

Basic physical quantities in the SI system, like mass and length.

Angle

A measure of rotation between two rays that share a common endpoint.