List of top Physics Questions

What is the gravitational force between two objects of masses \( m_1 = 10 \, \text{kg} \) and \( m_2 = 20 \, \text{kg} \), separated by a distance of \( r = 5 \, \text{m} \)? (Gravitational constant \( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))
What is the frequency of a wave with a wavelength of \( 2 \, \text{m} \) and a velocity of \( 4 \, \text{m/s} \)?
What is the energy stored in a capacitor of capacitance \( C = 10 \, \mu\text{F} \) when a potential difference of \( V = 20 \, \text{V} \) is applied across it?
A charge of 2 $\mu C$ is placed in an electric field of intensity \( 4 \times 10^3 \, \text{N/C} \). What is the force experienced by the charge?
A 5-ohm resistor is connected to a 10 V battery. Calculate the current flowing through the resistor.
If the volume of the tetrahedron, whose vertices are \( A(1, 2, 3), B(-3, -1, 1), C(2, 1, 3) \) and \( D(-1, 2, x) \), is \( \frac{11}{6} \) cubic units, then the value of \( x \) is:
If the angle between the line \( 2(x + 1) = y = z \) and the plane \( 2x - y + \sqrt{2} z + 4 = 0 \) is \( \frac{\pi}{6} \), then the value of \( \lambda \) is:
The particular solution of the differential equation, \[ x y \frac{dy}{dx} = x^2 + 2y^2 \quad \text{when} \quad y(1) = 0 \quad \text{is:} \]
If y = tan-1 ((2 + 3x) / (3 - 2x)) + tan-1 (4x / (1 + 5x2)), then
dy/dx =
The area enclosed between the parabola \( y^2 = 4x \) and the line \( y = 2x - 4 \) is:
If cos(12/13) + sin(P), then the value of P is:
If \( \mathbf{a} = 2\hat{i} + 2\hat{j} + 3\hat{k}, \mathbf{b} = -\hat{i} + 2\hat{j} + \hat{k} \) and \( \mathbf{c} = 3\hat{i} + \hat{j} \) are the vectors such that \( \mathbf{a} + \lambda \mathbf{b} \) is perpendicular to \( \mathbf{c} \), then the value of \( \lambda \) is:
Water is being poured at the rate of 36 m$^3$/min into a cylindrical vessel whose circular base is of radius 3 meters. Then the water level in the cylinder increases at the rate of:
If \( x^y + y^x = a^b \), then \( \frac{dy}{dx} \) at \( x = 1, y = 2 \) is:
Evaluate the integral: ∫ log((2 + x)2 + x) dx
Approximate value of \( \cos 59^\circ \) is:
If \( a(u + x^2) = x \) and \( y - x^3 = a^2 \), then \( \frac{dy}{dx} \) at \( x = 1 \) is:
For all real x, the minimum value of the function f(x) = (1 - x + x^2) / (1 + x + x^2) is:
Evaluate the definite integral: \[ \int_{0}^{\frac{\pi}{2}} \frac{dx}{1 + (\cot x)^{101}} = ? \]
If a(4 + x^2) = x + y - x^3 = a^3 * (dy/dx) at x = 1, then the value of (dy/dx) is:
A copper ball at \(80^\circ C\) is brought to \(60^\circ C\) in 5 minutes, with surrounding temperature at \(20^\circ C\). Find the temperature of the ball after 20 minutes.
A charge of \( 2 \, \mu\text{C} \) is placed in an electric field of intensity \( 4 \times 10^3 \, \text{N/C} \). What is the force experienced by the charge?
Two bodies of masses \( m_1 = 5 \, \text{kg} \) and \( m_2 = 10 \, \text{kg} \) are placed 2 meters apart. What is the gravitational force between them?
A mass of \( 0.5 \, \text{kg} \) is attached to a spring with a spring constant \( k = 200 \, \text{N/m} \). The mass is displaced by \( 0.1 \, \text{m} \) from its equilibrium position. What is the potential energy stored in the spring?
A fluid flows through a pipe with a varying cross-sectional area. If the velocity of the fluid is \( v_1 = 4 \, \text{m/s} \) at a point where the cross-sectional area is \( A_1 = 2 \, \text{m}^2 \), and the velocity at another point where the cross-sectional area is \( A_2 = 1 \, \text{m}^2 \) is \( v_2 \), what is the velocity \( v_2 \)?