List of practice Questions

Principal stresses occur where the shear stress is

If three forces acting in equilibrium at a point are 3 N, 4 N, and 5 N, the angle between the 3 N and 4 N forces is closest to:

The centroid of a rectangle of height h and width w is located at

For a thin plate shaped like a quarter circle, the polar moment of inertia at the center of the circle is given by

The moment of inertia of a rectangle with base b and height h about an axis through its centroid parallel to the base is

A mass undergoes simple harmonic motion (SHM) with an amplitude of 10 cm. Its maximum acceleration is 5 m/s\(^2\). The angular frequency \(\omega\) of the mass is

Impulse can be defined as

Which type of motion does a rigid body undergo about a fixed axis?

Mohr's Circle is used to

The bending moment diagram represents

Which of the following is not a type of support in structural analysis?

Shearing force in a beam tends to cause

The concept of mass moment of inertia is significant in the analysis of

The centroid of a composite plane figure is found by

The theorem relates the moment of inertia about any axis to the moment of inertia about a parallel axis through the centroid?

Polar moment of inertia is used primarily for calculating the stresses in

The equation F=kx describes a force that is

D'Alembert's Principle is used to

When several forces act at a point and their vector sum is zero, the forces are said to be

Evaluate the integral: \[ I = \int_{-5\pi}^{5\pi} \left(1 - \cos 2x \right)^{\frac{5}{2}} dx. \]

The area of the region enclosed by the curves \[ 3x^2 - y^2 - 2xy + 4x + 1 = 0 \] and \[ 3x^2 - y^2 - 2xy + 6x + 2y = 0 \] is:

If \[ x = 3 \left[ \sin t - \log \left( \cot \frac{t}{2} \right) \right], \quad y = 6 \left[ \cos t + \log \left( \tan \frac{t}{2} \right) \right] \] then find \( \frac{dy}{dx} \).