List of top Applied Mechanics and Design Questions on Trusses asked in GATE ME

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 shaft carries a helical spur gear. Which one of the following bearings can NOT be used to support it?
A structure, along with the loads applied on it, is shown in the figure. Self-weight of all the members is negligible and all the pin joints are friction-less. AE is a single member that contains pin C. Likewise, BE is a single member that contains pin D. Members GI and FH are overlapping rigid members. The magnitude of the force carried by member CI is ________________ kN (in integer).
A cylindrical disc of mass \( m = 1 \, \text{kg} \) and radius \( r = 0.15 \, \text{m} \) was spinning at \( \omega = 5 \, \text{rad/s} \) when it was placed on a flat horizontal surface and released (refer to the figure). Gravity \( g \) acts vertically downwards as shown in the figure. The coefficient of friction between the disc and the surface is finite and positive. Disregarding any other dissipation except that due to friction between the disc and the surface, the horizontal velocity of the center of the disc, when it starts rolling without slipping, will be ________________ m/s (round off to 2 decimal places).
Assuming the material considered in each statement is homogeneous, isotropic, linear elastic, and the deformations are in the elastic range, which one or more of the following statement(s) is/are TRUE?
The figure shows a schematic of a simple Watt governor mechanism with the spindle \( O_1O_2 \) rotating at an angular velocity \( \omega \) about a vertical axis. The balls at P and S have equal mass. Assume that there is no friction anywhere and all other components are massless and rigid. The vertical distance between the horizontal plane of rotation of the balls and the pivot \( O_1 \) is denoted by \( h \). The value of \( h = 400 \, \text{mm} \) at a certain \( \omega \). If \( \omega \) is doubled, the value of \( h \) will be ________________ mm.