Which instruments have uniform scale-a)Spring control instrumentb)Grav...
In spring control instrument, the controlling torque is given by,
Tc = Kcθ
Td ∝ I
At equilibrium position, TC = TD
⇒ I ∝ θ
Hence in spring control, the scale is uniform
In gravity control, a small weight is placed on an arm attached to the moving system. The position of this weight is adjustable. This weight produces a controlling torque due to gravity.
This controlling torque is given by,
Tc = Kgsinθ
Td ∝ I
At equilibrium position, TC = TD
⇒ I ∝ sinθ
Hence in gravity control, the scale is non uniform
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Which instruments have uniform scale-a)Spring control instrumentb)Grav...
Uniform Scale in Instruments
Uniform scale in instruments means that the instrument provides a linear output for a linear input. In other words, the scale markings on the instrument are equally spaced, and the deflection of the pointer or the reading on the display is directly proportional to the input quantity.
Spring Control Instrument
Spring control instruments are devices that use a spring to measure the force generated by the input quantity. The spring is attached to a pointer, and as the input force increases, the spring stretches and the pointer moves along a calibrated scale. Examples of spring control instruments include spring balances, spring-loaded pressure gauges, and spring-loaded thermometers.
Uniform Scale in Spring Control Instruments
Spring control instruments have a uniform scale because the deflection of the pointer is directly proportional to the input force. As the spring stretches, the pointer moves a fixed distance for a given increase in force, and the scale markings are evenly spaced to reflect this linear relationship. Therefore, the response of a spring control instrument is linear over its entire range, and the scale is uniform.
Gravity Control Instrument
Gravity control instruments are devices that use the force of gravity to measure the input quantity. These instruments rely on the movement of a mass or a pendulum to indicate the input value. Examples of gravity control instruments include pendulum clocks, balance scales, and gravimeters.
Non-Uniform Scale in Gravity Control Instruments
Gravity control instruments do not have a uniform scale because the deflection of the mass or the pendulum is not directly proportional to the input quantity. The deflection depends on the weight and the geometry of the moving parts, as well as the strength of the Earth's gravity. Therefore, the response of a gravity control instrument is non-linear, and the scale is non-uniform.
Conclusion
In summary, spring control instruments have a uniform scale because their response is linear and proportional to the input force, while gravity control instruments have a non-uniform scale because their response is non-linear and depends on the weight and geometry of the moving parts. Therefore, the correct answer to the given question is option 'A': Spring control instruments have a uniform scale.
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