# GATE2016-2-36

The rod $AB$, of length $1$ $m$, shown in the figure is connected to two sliders at each end through pins. The sliders can slide along $QP$ and $QR$. If the velocity $VA$ of the slider at $A$ is $2$ $m/s$, the velocity of the midpoint of the rod at this instant is ___________ $m/s$. recategorized

## Related questions

The system shown in the figure consists of block A of mass $5$ $kg$ connected to a spring through a massless rope passing over pulley B of radius $r$ and mass $20$ $kg$. The spring constant $k$ is $1500$ $N/m$. If there is no slipping of the rope over the pulley, the natural frequency of the system is_____________ $rad/s$.
A mass of $2000$ $kg$ is currently being lowered at a velocity of $2$ $m/s$ from the drum as shown in the figure. The mass moment of inertia of the drum is $150$ $kg$-$m^2$. On applying the brake, the mass is brought to rest in a distance of $0.5$ $m$. The energy absorbed by the brake (in $kJ$) is __________
The forces $F_1$ and $F_2$ in a brake band and the direction of rotation of the drum are as shown in the figure. The coefficient of friction is $0.25$. The angle of wrap is $3\pi /2$ radians. It is given that $R$ = $1$ $m$ and $F_2$ = $1$ $N$. The torque (in $N$-$m$) exerted on the drum is _________
A single degree of freedom mass-spring-viscous damper system with mass $m$, spring constant $k$ and viscous damping coefficient $q$ is critically damped. The correct relation among $m$, $k$, and $q$ is $q=\sqrt{2km} \\$ $q=2\sqrt{km} \\$ $q=\sqrt{\dfrac{2k}{m}} \\$ $q=2\sqrt{\dfrac{k}{m}}$