$2\mathrm{.}7$ A shaft encoder is to be used with a $50$ mm radius tracking wheel to monitor linear displacement. If the encoder produces $256$ pulses per revolution, what will be the number of pulses produced by a linear displacement of $200$ mm $?$

$2\mathrm{.}8$ A rotary variable differential transformer has a specification which includes the following information:

Ranges $+-30,$ linearity error $+-0\mathrm{.}5\%$ full range

$+-60,$ linearity error $+-2\mathrm{.}0\%$ full range

Sensitivity: $1\mathrm{.}1(m\frac{V}{V}$ input$)/$degree

Impedance: primary $750,$ secondary $2000$

What will be $($a$)$ the error in a reading of $40$ due to non$-$linearity when the RDYT is used on the $+-60$ range, and $($b$)$ the output voltage change that occurs per degree if there is an input voltage of $3$ V $?$

$2\mathrm{.}9$ What are the advantages and disadvantages of the plastic film rype of potentiometer when compared with the wire$-$wound potentiometer?

$2\mathrm{.}10$ A pressure sensor consisting of a diaphragm with strain gauger bonded to its surface has the following information in its specification:

Ranges: $0$ to $1400kP2,0$ to $35000$ kPa

Non$-$linearity error: $+-0\mathrm{.}15\%$ of full range

Hysteresis error: $+-0\mathrm{.}05\%$ of full range

What is the total error due to non$-$linearity and hysteresis for a reading of $1000$ kPa on the $0$ to $1400$ kPa range?

$2\mathrm{.}11$ The water level in an open vessel is to be monitored by a differential pressure oell responding to the difference in pressure between that at the base of the vessel and the atmosphere. Determine the range of differential pressures the cell will have to respond to if the water level can vary between zero height above the cell measurement point and $2$ m above it$.$