The rotor of an aeroplane engine has a mass moment of inertia $1.0 \mathrm{~kg} \mathrm{~m}^2$. The engine rotates at a speed of 500 RPM in the clockwise direction if viewed from the front of the aeroplane. If the aeroplane while flying at $1200 \mathrm{~km} / \mathrm{hr}$ turns with a radius of 2 km at same elevation, then the magnitude of the gyroscopic moment exerted by the rotor on the aeroplane structure in N m is

A truss structure is loaded as shown in the figure below. Among the options given, which member in the truss is a zero-force member?

A ram in the form of a rectangular body of size $l = 9 \text{ m}$ and $b = 2 \text{ m}$ is suspended by two parallel ropes of lengths $7 \text{ m}$. Assume the center-of-mass of the body is at its geometric center and $g = 9.81 \text{ m/s}^2$. For striking the object P with a horizontal velocity of $5 \text{ m/s}$, what is the angle $\theta$ with the vertical from which the ram should be released from rest?

A rigid massless tetrahedron is placed such that vertex O is at the origin and the other three vertices A, B, and C lie on the coordinate axes as shown in the figure. The body is acted on by three point loads, of which one is acting at A along x-axis and another at point B along y-axis. For the body to be in equilibrium, the third point load acting at point O must be