GATE IN 2012 Question Paper (12-Feb-2012) (Shift-2)

A U-tube manometer of tube diameter $D$ is filled with a liquid of zero viscosity. If the volume of the liquid filled is $V$, the natural frequency of oscillations in the liquid level about its mean position, due to small perturbations, is

The open loop transfer function of a unity gain negative feedback control system is given by $G(s)=\frac{s^2+4s+8}{s(s+2)(s+8)}$. The angle $\theta$, at which the root locus approaches the zeros of the system, satisfies

With $10$ V dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed:

(i) $1$ $\Omega$ connected at port B draws a current of $3$ A

(ii) $2.5$ $\Omega$ connected at port B draws a current of $2$ A

The deflection profile $y(x)$ of a cantilever beam due to application of a point force $F$ (in Newton), as a function of distance $x$ from its base, is given by $y(x)=0.001F{x}^2(1-\frac{x}{3})$ m. The angular deformation $\theta$ at the end of the cantilever is measured by reflecting a laser beam off a mirror M as shown in the figure.

The deflection profile $y(x)$ of a cantilever beam due to application of a point force $F$ (in Newton), as a function of distance $x$ from its base, is given by $y(x)=0.001F{x}^2(1-\frac{x}{3})$ m. The angular deformation $\theta$ at the end of the cantilever is measured by reflecting a laser beam off a mirror M as shown in the figure.