Two plates of thickness 10 mm each are to be joined by a transverse fillet weld on one side and the resulting structure is loaded as shown in the figure below. If the ultimate tensile strength of the weld material is 150 MPa and the factor of safety to be used is 3, the minimum length of the weld required to ensure that the weld does NOT fail is ____________ mm (rounded off to 2 decimal places).
An offset slider-crank mechanism is shown in the figure below. The length of the stroke of the slider is __________ mm (rounded off to nearest integer).
The system shown in the figure below consists of a cantilever beam (with flexural rigidity \( EI \) and negligible mass), a spring (with spring constant \( K \) and negligible mass) and a block of mass \( m \). Assuming a lumped parameter model for the system, the fundamental natural frequency (\( \omega_n \)) of the system 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?
\[ {Given: } F = 1000\,{N} \]
A rigid circular disc of radius \(r\) (in m) is rolling without slipping on a flat surface as shown in the figure below. The angular velocity of the disc is \(\omega\) (in rad/ssuperscript{-1}). The velocities (in m/ssuperscript{-1}) at points 0 and A, respectively, are:
