The angle turned by a wheel while it starts from rest and accelerates at constant rate of
3 rad/s2 for an interval of 20 sec is
(B) 600 rad
(A) 900 rad. (C) 1200 rad
(D) 300 rad
To find the angle turned by the wheel during the given interval, we can use the formula for angular displacement:
θ = ω_i * t + (1/2) * α * t^2
where:
θ = angular displacement (the angle turned by the wheel)
ω_i = initial angular velocity (0 rad/s as it starts from rest)
α = angular acceleration (given as 3 rad/s^2)
t = time interval (given as 20 sec)
Plugging in the values:
θ = 0 * 20 + (1/2) * 3 * (20)^2
θ = 0 + 0.5 * 3 * 400
θ = 0 + 600
θ = 600 rad
So, the angle turned by the wheel during the 20-second interval is 600 rad.
The correct answer is (B) 600 rad.
Stress due to change in temperature developed in a bar depends upon
(A) coefficient of thermal expansion
(B) thermal conductivity
(C) density
(D) Poisson's ratio
(A) coefficient of thermal expansion
The stress developed in a bar due to a change in temperature depends on the coefficient of thermal expansion. When a material is subjected to a temperature change, it tends to expand or contract. This thermal expansion or contraction can lead to the development of stress within the material. The coefficient of thermal expansion is a material property that represents how much a material will expand or contract per unit length per degree temperature change.
Thermal conductivity (B) is a property that represents a material's ability to conduct heat, but it is not directly related to the stress developed due to temperature changes.
Density (C) and Poisson's ratio (D) are also material properties, but they are not directly involved in determining the stress due to temperature changes. Density is related to the mass per unit volume of a material, and Poisson's ratio is a measure of a material's lateral contraction when it is stretched in one direction.
Therefore, the correct answer is (A) coefficient of thermal expansion
Strength of the beam depends on
(A) Bending moment
(B) Density
(C) Section modulus (D) c.g. of the section
The strength of a beam primarily depends on:
(C) Section modulus
The section modulus is a geometric property of the cross-sectional shape of the beam that directly relates to its resistance to bending. It is a measure of how far the outer fibers of the beam are from its neutral axis (centroid), which is the axis with no stress during bending. A larger section modulus indicates a beam with greater resistance to bending and, therefore, higher strength.
(A) Bending moment
The bending moment is the moment or force applied to a beam that causes it to bend. While the bending moment is an important factor in analyzing the structural behavior of a beam, it is not a direct measure of the beam's strength. The bending moment helps in calculating the internal stresses and deflections in the beam, which, in turn, affects its strength.
(B) Density
Density is a material property related to mass per unit volume and does not directly determine the strength of a beam. However, the material's density can indirectly influence the weight and mass of the beam, affecting its overall performance in certain applications.
(D) c.g. of the section
The "c.g." mentioned likely refers to the centroid or center of gravity of the section. The centroid is important in structural analysis, but it is not the primary factor that determines the strength of a beam. The centroid helps in calculating various geometric properties like section modulus, but it is not the sole indicator of strength.
In conclusion, the strength of a beam depends on its Section modulus (C), which is a critical geometric property related to its resistance to bending.
A reversible heat engine working at the rate of 100 kW has an efficiency of 20%. The magnitudes of heat transfer rate from the source and to the sink in kW would be, respectively,
(A) 200, 100
(C) 500, 400
(B) 300, 200
(D) 1000, 900.
To find the magnitudes of the heat transfer rate from the source and to the sink, we can use the efficiency formula for a heat engine:
Efficiency = (Work output) / (Heat input)
Given that the heat engine has an efficiency of 20% (0.20) and works at the rate of 100 kW, we can calculate the heat input and work output.
Efficiency = (Work output) / (Heat input)
0.20 = Work output / 100 kW
Work output = 0.20 * 100 kW
Work output = 20 kW
Now, we know that the work output of the engine is 20 kW. For a reversible heat engine, the work output is equal to the heat input minus the heat output (heat rejected to the sink):
Work output = Heat input - Heat output
20 kW = Heat input - Heat output
We are also given that the heat engine works at the rate of 100 kW. This means the heat input is 100 kW. Now, we can find the heat output (heat rejected to the sink):
Heat output = Heat input - Work output
Heat output = 100 kW - 20 kW
Heat output = 80 kW
So, the magnitudes of the heat transfer rate from the source and to the sink are 100 kW and 80 kW, respectively.
The correct answer is (A) 200, 100.
The friction between objects that
stationary is called
(A) static friction
(B) rolling friction
(C) kinetic friction
(D) dynamic friction
(A) static friction
Static friction is the type of friction that occurs between two surfaces in contact when there is no relative motion between them, i.e., when the objects are stationary or at rest with respect to each other. It prevents the objects from sliding or moving when an external force is applied to them.
On the other hand, kinetic friction (C), also known as dynamic friction (D), is the friction that occurs between objects in contact when they are moving relative to each other.
Rolling friction (B) is a specific type of friction that occurs when an object, such as a wheel or ball, rolls over a surface.
In this case, since the objects are stationary, the friction between them is static friction (A).
Fatigue of a component is due to
(A) cyclic load
(B) static load
(C) constant heating
(D) collision
(A) cyclic load
Fatigue of a component is due to cyclic load. Fatigue is a phenomenon where a material or component fails when subjected to repeated loading and unloading cycles, even if the applied loads are below the material's ultimate strength. Over time, the repeated cyclic loading leads to the accumulation of microcracks and damage, eventually resulting in failure.
Static load (B) refers to a constant, unchanging load applied to a component without any cycling.
Constant heating (C) refers to the application of a consistent and constant heat source to a component, which may lead to thermal stress but not fatigue failure.
Collision (D) is a general term for an impact between two objects. While collisions can cause damage to components, they are not specifically related to fatigue failure, which occurs due to cyclic loading.
Thus, the correct answer is (A) cyclic load.
In diesel engines, the duration between the time of injection and ignition, is known as
(A) pre-ignition period
(B) delay period (C) ignition period
(D) búrning period
(B) delay period
In diesel engines, the duration between the time of fuel injection and the start of combustion or ignition is known as the "delay period" (B). During this delay period, the fuel is injected into the combustion chamber as a high-pressure spray, and it needs time to mix with the high-temperature, high-pressure air in the cylinder before ignition can occur. The delay period is a critical phase in diesel engine operation and affects the combustion process and engine performance. Once the fuel is adequately mixed with the air and reaches the auto-ignition temperature, combustion starts, and the engine's power stroke begins.
If V; be the inlet absolute velocity to blades, V be the tangential blade velocity and a be the nozzle angle, then for maximum blade efficiency for single-stage impulse turbine
The inlet absolute velocity (V;) and the tangential blade velocity (V) should be in the same direction. In other words, they should have the same sign.
The nozzle angle (α) should be such that the relative velocity (Vr) of the fluid exiting the nozzle is purely axial (i.e., no tangential component).
The relative velocity (Vr) is given by the vector sum of the inlet absolute velocity (V;) and the tangential blade velocity (V):
Vr = V; + V
For maximum blade efficiency, we want the relative velocity (Vr) to be purely axial, meaning there is no tangential component (Vθ). Mathematically, this condition is expressed as:
Vθ = 0
Now, Vθ is given by:
Vθ = V * tan(α)
Since we want Vθ to be zero, we need the nozzle angle (α) to be zero:
α = 0
So, for maximum blade efficiency in a single-stage impulse turbine:
V; and V should have the same sign.
The nozzle angle (α) should be zero.
These conditions ensure that the fluid exits the nozzle purely axially, and there is no tangential component of velocity at the exit, maximizing the energy transfer to the turbine blades and achieving the highest blade efficiency.
The friction between objects that
stationary is called
(A) static friction
(B) rolling friction
(C) kinetic friction
(D) dynamic friction
(A) static friction
Static friction is the type of friction that occurs between two surfaces in contact when there is no relative motion between them, i.e., when the objects are stationary or at rest with respect to each other. It prevents the objects from sliding or moving when an external force is applied to them.
On the other hand, kinetic friction (C), also known as dynamic friction (D), is the friction that occurs between objects in contact when they are moving relative to each other.
Rolling friction (B) is a specific type of friction that occurs when an object, such as a wheel or ball, rolls over a surface.
In this case, since the objects are stationary, the friction between them is static friction (A).
The process of supplying the intake air to the engine cylinder at a density more than the density of the surrounding atmosphere is known as
(A) scavenging
(B) detonation
(C) supercharging
(D) polymerisation
(C) supercharging
The process of supplying the intake air to the engine cylinder at a density higher than the density of the surrounding atmosphere is known as supercharging. Supercharging involves compressing the intake air using a mechanical device (such as a supercharger) before it enters the engine cylinder. By increasing the air density, the engine can burn more fuel and produce more power, improving the engine's overall performance.
The other options are unrelated to the process of supplying intake air at a higher density:
(A) Scavenging is the process of purging exhaust gases from the engine cylinder to improve combustion efficiency.
(B) Detonation is an undesirable phenomenon in internal combustion engines where the air-fuel mixture ignites too early and causes a rapid, uncontrolled combustion.
(D) Polymerization is a chemical process unrelated to engine operations and refers to the combination of monomers to form a polymer.
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