A horizontal beam of length 1200 mm is pinned at the left end and is resting on a roller at the other end as shown in the figure. A linearly varying distributed load is applied on the beam. The magnitude of maximum bending moment acting on the beam is _______ N.m. (round off to 1 decimal place)

The figure shows a thin cylindrical pressure vessel constructed by welding plates together along a line that makes an angle $\alpha = 60^\circ$ with the horizontal. The closed vessel has a wall thickness of 10 mm and diameter of 2 m. When subjected to an internal pressure of 200 kPa, the magnitude of the normal stress acting on the weld is _________ MPa (rounded off to 1 decimal place).

The change in kinetic energy $\Delta E$ of an engine is $300$ J, and minimum and maximum shaft speeds are $\omega_{min} = 220$ rad/s and $\omega_{max} = 280$ rad/s, respectively. Assume that the torque-time function is purely harmonic. To achieve a coefficient of fluctuation of $0.05$, the moment of inertia (in kg.m$^2$) of the flywheel to be mounted on the engine shaft is

A linear spring-mass-dashpot system with a mass of 2 kg is set in motion with viscous damping. If the natural frequency is 15 Hz, and the amplitudes of two successive cycles measured are 7.75 mm and 7.20 mm, the coefficient of viscous damping (in N.s/m) is