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

A double convex lens is used to couple a laser beam of diameter 5 mm into an optical fiber with a numerical aperture of 0.5. The minimum focal length of the lens that should be used in order to focus the entire beam into the fiber is

An analog voltmeter uses external multiplier settings. With a multiplier setting of 20 k$\Omega$, it reads 440 V and with a multiplier setting of 80 k$\Omega$, it reads 352 V. For a multiplier setting of 40 k$\Omega$, the voltmeter reads

The open loop transfer function of a unity negative feedback control system is given by $G(s)=\frac{150}{s(s+9)(s+25)}$ The gain margin of the system is

A dynamometer arm makes contact with the piezoelectric load cell as shown. The g-constant of the piezoelectric material is $50\times 10^{-3}$ Vm/N and the surface area of the load cell is $4$ cm${}^2$. If a torque $\tau =20$ Nm is applied to the dynamometer, the output voltage $V_o$ of the load cell is

Water (density: $1000$ kgm${}^{-3}$) stored in a cylindrical drum of diameter $1$ m is emptied through a horizontal pipe of diameter $0.05$ m. A pitot-static tube is placed inside the pipe facing the flow. At the time when the difference between the stagnation and static pressures measured by the pitot-static tube is $10$ kPa, the rate of reduction in water level in the drum is,