To find the grinding speed (linear velocity) of the wheel, we need to use the relationship between linear velocity, angular velocity, and the radius of the wheel. The given rotational speed is in revolutions per minute (rpm), which needs to be converted to radians per second to calculate the angular velocity. The diameter needs to be converted to radius and then to meters.
Radius \(R = D/2\)
\[ R = \frac{150 \text{ mm}}{2} = 75 \text{ mm} \]Convert millimeters to meters:
\[ R = 75 \times 10^{-3} \text{ m} = 0.075 \text{ m} \]Angular velocity (\(\omega\)) is given by:
\[ \omega = \frac{2 \pi N}{60} \text{ rad/sec} \] \[ \omega = \frac{2 \pi \times 3000}{60} \] \[ \omega = 2 \pi \times 50 \] \[ \omega = 100 \pi \text{ rad/sec} \]The linear velocity (\(V\)) is related to angular velocity (\(\omega\)) and radius (\(R\)) by the formula:
\[ V = \omega R \] \[ V = (100 \pi \text{ rad/sec}) \times (0.075 \text{ m}) \] \[ V = 7.5 \pi \text{ m/sec} \]Correct Option: A) 7.5π m/sec
The question asks about the machining allowance in die casting. To answer this, we need to understand the characteristics of the die casting process and the quality of the parts it produces.
D) Not provided — In die casting, parts are produced with high dimensional accuracy and excellent surface finish due to the use of high pressure and precision dies. This often eliminates the need for subsequent machining operations, meaning that little to no machining allowance is provided.
The question asks to identify the type of manufacturing operation that grinding represents. We need to understand the primary purpose and characteristics of grinding to classify it correctly among the given options.
Correct Option: C) Surface finishing operation
The question asks to identify the sheet metal operation where a tab is formed without removing any material. This requires understanding the basic definitions of various sheet metal cutting and forming processes.
Correct Option: B) Lancing
The question asks about the specific welding method used for steel rails. This requires knowledge of different welding processes and their typical applications. Steel rails are large, heavy components that require a strong, durable, and reliable weld, often performed in situ. We need to identify the welding process best suited for such an application.
B) Thermit welding is a chemical welding process that uses an exothermic reaction to produce molten metal, which then fuses the parts to be joined. It is particularly well-suited for welding large sections like railway tracks and heavy structural components because it can produce a large volume of molten metal quickly and effectively in the field, creating strong, durable joints.
The question asks for the fundamental principle on which a D.C. generator operates. Understanding the function of a generator is key to identifying the correct physical law.
Correct Option: A) Electromagnetic Induction. A D.C. generator works on the principle of electromagnetic induction, where mechanical energy is converted into electrical energy by inducing an electromotive force (EMF) in a conductor moving in a magnetic field.
The question asks about the primary application of thermal relays. Thermal relays are protective devices designed to safeguard electrical equipment from damage caused by overheating due to excessive current. Understanding their operating principle and typical applications helps identify the correct option.
A) motor starters — Thermal relays are specifically designed for overload protection of electric motors. They protect the motor windings from overheating due to sustained overcurrents, which can occur during starting or due to mechanical overloads. They are an integral part of most motor starter circuits.
The question asks to identify the most commonly used moderator in a nuclear reactor. A moderator's function is to slow down fast neutrons produced during fission to thermal energies, making them more likely to cause further fission reactions. We need to evaluate the given options based on their properties as neutron moderators.
D) heavy water — Heavy water (\(\text{D}_2\text{O}\)) is an excellent moderator because deuterium has a low atomic mass, allowing for efficient slowing down of neutrons, and a very low neutron absorption cross-section, meaning it doesn't absorb many neutrons that are needed for the chain reaction. This allows reactors using heavy water to operate with natural (unenriched) uranium, making it a very important and commonly used moderator in certain reactor types.
The question asks about the primary mechanism for overspeed protection in a generator. We need to identify the component specifically designed to regulate the speed of the prime mover driving the generator.
Correct Option: A) Governor. A governor is a crucial component in power generation systems that automatically regulates the speed of the prime mover (like a turbine) driving the generator. It ensures that the generator operates at a constant speed to maintain a stable output frequency and protects against dangerous overspeed conditions by controlling the fuel/steam/water input.
The question asks to identify the type of motor that does not have windings on its rotor. We need to recall the construction principles of each motor type listed in the options.
Based on these characteristics, the hysteresis motor is the one that uniquely lacks windings on its rotor.
C) Hysteresis — The rotor of a hysteresis motor is a smooth cylinder of hard magnetic material without any windings. It operates on the principle of continuous magnetic hysteresis loss induced in the rotor by the rotating magnetic field of the stator.