Shock resisting steel should have higher
ISRO Scientist or Engineer Mechanical 2014
For the following questions answer them individually
Let $$A = \begin{bmatrix}0 & 0 & -1 \\0 & -1 & 0 \\-1 & 0 & 0 \end{bmatrix}$$ The only correct statement about the matrix A is
Let M be a $$3 \times 3$$ matrix satisfying:
$$M \begin{bmatrix}0\\1\\0 \end{bmatrix} = \begin{bmatrix}-1\\2\\3 \end{bmatrix}, M \begin{bmatrix}1\\-1\\0 \end{bmatrix} = \begin{bmatrix}1\\1\\-1 \end{bmatrix}$$, and $$M \begin{bmatrix}1 \\1 \\1 \end{bmatrix} = \begin{bmatrix}0 \\0 \\12 \end{bmatrix}$$. Then the sum of the diagonal entries of M is:
Angle made between vector $$\overrightarrow{C} = \overrightarrow{2i} - \overrightarrow{3j} + \overrightarrow{4k}$$ and the Z-axis
Which of the following is the correct definition of the Reynolds number?
Where $$\rho$$ = fluid density, U = velocity, L = Length and $$\mu$$ = kinematic viscosity
A steam engine intakes 100gm of steam at $$100^\circ C$$ per minute and cools it down to $$20^\circ C$$ . Calculate the heat rejected by the steam engine per minute. (consider Latent Heat of vaporization of steam = 540 cal/gm and Cp = 1 cal/gm/$$^\circ C$$
A heat engine operates between a cold reservoir at temperature T2 = 300 K and a hot reservoir at Temperature T1. It takes 200J of heat from the hot reservoir and deliver 120J of heat to the cold reservoir in a cycle. Whatwill be the efficiency of the engine?
Two bodies A and B having equal surface area are maintained at temperatures $$10^\circ C$$ and $$20^\circ C$$. The energy of thermal radiations emitted in a given time by A and B are in the ratio:
A hot liquid is kept in a big room. Its temperature($$\theta$$) is plotted as a function of time(t), which of the following curve may represent the plot?
Aluminum crystal structure is
A spherical balloonis filled with $$3536 \pi$$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of $$70 \pi$$ cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 50 minutes after the leakage began is
Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3% each, then error in the value of resistance of the wire is
A purse contains 4 copper coins and 3 silver coins. A second purse contains 6 copper coins and 4 silver coins. A purse is chosen randomly and a coin is taken out of it. What is the probability that it is a copper coin?
The Grash of number, Gr is defined as:(where g is gravitational acceleration, $$\beta$$ is volumetric thermal expansion coefficient, $$\triangle T$$ is temperature difference, L is characteristic length, $$\mu$$ is the viscosity and v is kinematic viscosity.
The Rayleigh number Ra, is defined as: (where Gr is Grashof Number, Pr is Prandtl Number and Re is Reynold Number)
For two bodies having direct impact, Co-efficient of restitution is given by
A perfect frame is that which satisfies the equation (Assume n = No. Of members and j = No. Of joints)
Tension in the cable supporting a lift of weight ‘W’ and having an acceleration of ‘a’ while going upward is (gis acceleration due to gravity)
A body A of weight 10 Kg with its C.G. 25 cm from the axis of rotation is to be balanced by another body B of weight 5 Kg. The radius at which the C.G. of weight B should be placed is
In case of a horizontal beam loaded under bending, the point of inflexion or contra flexure corresponds to a point on the beam, where
Shaft AB is 3 meter long andis free at the left end and fixed torsionally at the right end. It is subjected to variable torque as shown in the figure. The intensity of the torsional loading is given by q = 2x. The internal ‘ T, as a function of x is
A cantilever beam 6 meter long as shown in figure is subjected to a linearly varying loading which has a maximum ordinate of 360 N/m at the fixed end on the right. The moment as a function of x is
Consider the beam shown in figure. The beam is simply supported at its left end A and fixed at its right end B. It carries a load that varies in intensity from zero at support A to ‘w’ at support B according to the relation $$w_x = (x/L)w$$. The reaction component at A is
A 4 meter long solid circular cylindrical shaft transmits 1600 kW at 500 rpm. The endurancelimit of the material is 210 MPa and a factor of safety of 3 is to be used with respect to fatigue failure. Use G= 77.5 GPa. The design diameter ‘D’ of the shaft in metre is
A. three bar truss to resist a service load P= 100 kN is shown in the figure. Use a load factor of 2 and consider all three members to have equal cross-sectional areas. The yield stress of the material of which the members are fabricated is 400 MPa. The area of cross section of each truss member is
A thin-walled cylinder with closed ends for which inner radius is 0.50 meter & outer radius is 0.52 meter, is subjected to internal pressure 2 MPa. The absolute maximum shearing stress on the inner surface of the cylinder shall be
A 0.75 meter aluminium bar $$25 \times 10^{-4} m^2$$ in cross-sectional area is attached to a 0.50 meter steel bar $$15 \times 10^{-4} m^2$$ in cross-sectional area, as shown in the figure. Take E (Young’s modulus) value of 200 GPa for steel & 70 GPa for aluminum. Total shortening due to an axial compressive force of 175 KN is
Member CD of the assembly shown is an aluminium bar 0.80 meter long. Cross-sectional dimension of the bar is such that, its width is three times its thickness. For functional design of the bar CD, the allowable axial stress is 70 MPa, and the total elongation is not to exceed 0.72 mm. E value for aluminium is 70 GPa. Assume the connection at C does not reduce the net area of the bar. The thickness of the bar in metre is
A solid steel shaft transmits 40kW of power at a speed of $$\frac{75}{\pi} Hz$$. The internal torque needed in the shaft is
A simply supported beam is shown in the figure below. The location of the point of maximum moment in the beam from reaction $$R_L$$ is
A 20 KN weight is suspended by two wires as shown in the figure. The length of each wire is 2 meter. The steel wire (E value 200 GPa) has an cross-sectional area of $$60 \times 10^{-6} m^2$$ and the aluminum wire(E value 70 GPa) has an cross-sectional area of $$120 \times 10^{-6} m^2$$, The stress in aluminum wire is
A bar of bronze and a bar of steel are placed between two immovable supports, A & B as shown in the figure. The physical constants are: (where L= length of bars, A = cross-sectional area, $$\alpha =$$ linear co-efficient of thermal expansion, E= Young’s modulus)
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The stresses in the steel & bronze, when temperature drops by $$50^\circ C$$ is
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Arigid bar with wires at B & C is shown in the figure below. The cross sectional area of the wire at Bis $$3 \times 10^{-4} m^2$$ and at C is $$2 \times 10^{-4} m^2$$. The wires are elasto- plastic with strength 250 MPa and E value 200 GPa. The ultimate load P that can be applied to the rigid bar, as shown is
The fundamental natural frequency of the cantilever beam with point load P acting at thefree end, in rad/sec is
The structure which has the highest packing of atoms
Elastic stress distribution in the cross section of a curved beam under pure bending is
Dimension of shaft is $$100_{0.00}^{+0.01}$$ and and corresponding Hole diameter is $$100_{0.01}^{+0.02}$$. The maximum material condition of the fit is
Match List 1 with List-II and select the correct answer.
In case of steady incompressible laminar viscous flow between two stationary parallel plates, the velocity distribution is
Two pipe lines of equal length are connected in series. The diameter of secondpipe is two times thatof first pipe, the ratio of head loss between first and second pipe is
The velocity potential function $$\varnothing$$ satisfy the Laplace equation :
$$\frac{\delta^2 \varnothing}{\delta x^2} + \frac{\delta^2 \varnothing}{\delta y^2} + \frac{\delta^2 \varnothing}{\delta z^2} = 0$$. Then the flow is
For a two dimensional potential flow, the velocity potential is given by:
$$\varnothing = 4x(3y - 4)$$ The numerical value of stream function at the point(2, 3) is
The velocity distribution in a turbulent boundary layeris given by $$\frac{u}{v} = \left(\frac{y}{\delta}\right)^{\frac{1}{7}}$$. What is the displacement thickness $$\delta^*$$
The specific weight W of ocean water changes according to the equation $$W = W_o + C \surd h. W_o = $$Specific weight of ocean water at free surface and C is a constant. The pressure as a function of depth h is given by
The model of a propeller, 3 m diameter, cruising at 10 m/sec in air, is tested in a wind tunnel on a 1:10 scale model. If thrust of 50 N is measured on the model at 5 m/sec wind speed, then thrust on prototype will be
As shown in Fig. below, an ideal gas is confined to a cylinder by a piston. The piston is pushed down slowly so that the gas temperature remains at $$27^\circ C$$. During the compression, 900 J of work is done on the gas. Find the entropy change of the gas.
Determine the number of degrees of freedom used in the analysis of the mechanical system of below mentioned Figure.
The difference in the Potential energies between two arbitrary positions downward displacements X1 and X2. (X2 > X1)
Water having kinematic viscosity of 0.01 stoke flows at a velocity of 2 m/sec in a pipe of 15 cm diameter. For dynamic similarity, the velocity of oil of kinematic viscosity of 0.03 stoke in a pipe of same diameter will be
An inclined plate 2 m long and 1 m widelies with its length inclined at $$45^\circ$$ to the surface of water and its nearest edge is 1 m below it. If specific weight of water is 1000kg/m$$^3$$, then total pressure force on the plate (in kg) is approximately
A liquid of density 1200 kg/m$$^3$$ is flowing steadily through a tube of varying cross section as shown below.Thecross section at point A is 1 cm$$^2$$ and at Bis 20 mm$$^2$$. The points A and B are in the same horizontal plane. The speed of liquid at point A is 10 cm/sec. The difference of pressure at A and B is
A wooden plank ( sp. gravity = 0.5) of 1 m $$\times$$ 1m $$\times$$ 0.5 m floats in water with 1.5 kN load on it with 1 mx 1m surface horizontal. The depth of plank lying below water surface shall be
Circulation is defined as the line integral of tangential component of velocity about a
Unstable equilibrium of a floating body implies
Viscosity has the dimension of
Which of the following flow is rotational (where u and v are velocity components in x and y directions respectively)
A pump running at 1000 rpm consumes 1KW and generates head Of 10m of water. When it is operated at 2000rpm, its power consumption and head generated would be
For irrotational fluid flow curl of velocity vector is
In the figure shown below, the relative velocity of link 1 with respect to link 2 is 15 m/s. The link 2 rotates at a constant speed of 150 rpm. The magnitude of coriolis component of acceleration of link 1 is
An oil of kinematic viscosity of 0.5 stokes flow through a pipe of 20 cm diameter. What is the velocity if the flow is critical?
A vertical air stream flowing at a velocity of 100 m/s supports a ball of 60 mm in diameter. Taking the density of air as 1.2 kg/m$$^3$$ and kinematic viscosity as 1.6 stokes, the weight of the ball that is supported is (if coefficient of drag $$C_D = 0.8$$)
The velocity distribution for flow overa flat plate is given by $$U = \left(\frac{3}{4}\right)y - y^2$$ in which u is the velocity in m/s at a distance y meter above the plate. If the dynamic viscosity of the fluid is 10 poise, then the shear stress at 0.2 m is
Determine $$M_{eq}$$ and $$K_{eg}$$ for the system in below Fig., when X, the downward displacement of the block, measured from the system's equilibrium position, is used as the generalized coordinate. Take I as the M.I. of the wheel.
The system described by the following governing equation of motion, will have how many natural frequencies?
$$\begin{bmatrix}m & 0 \\0 & m \end{bmatrix}\begin{bmatrix}\ddot{x1} \\\ddot{x2} \end{bmatrix} + \begin{bmatrix}2k & -k \\-k & 3k \end{bmatrix}\begin{bmatrix}x1 \\x2 \end{bmatrix} = \begin{bmatrix}0 \\0 \end{bmatrix}$$
Find out the correct free body diagram for the middle mass for the given spring- mass system in below figure.
For what value of m (mass) will resonance occur for the spring-mass system given below with the given spring constants?
Surface A in the figure is coated with white paint and maintained at temperature of $$27^\circ C$$. It is located directly opposite to surface B which can be considered a black body and maintained at temperature of $$727^\circ C$$. Calculate the amount of heat that needs to be removed from surface A per unit area to maintain its constant temperature. (consider emissivity of the white paint = 1 and view factor = 1, $$\sigma$$ = Stefan — Boltzmann constant)
The convective heat transfer coefficient h is defined by the relationship (m=mass, Cp=specific heat, k= conductivity, q = heat flow rate, Nu = Nusselt Number, L = Thickness, $$\triangle T$$ = Temperature difference)
The figure below shows a cross section through an insulated heating pipe which is made from steel (k=45 W/m K) with an inner radius of 150mm and outer radius of 155 mm. The pipe is coated with 100 mm thickness of insulation having thermal conductivity of k = 0.06 W/m K. Air at inlet temperature $$Ti = 60^\circ C$$ flow through the pipe has a value of convective coefficient hi = 35 W/m$$^2$$ K. The outside surface of the pipe is surrounded by air which is at $$15^\circ C$$ and convective heat transfer coefficient on this surface has a value of ho = 10 W/m$$^2$$ K. Find the critical insulation radius?
Graphene is
A bar of Cu of length 75 cm and a steel bar of 125 cm length are joined together end to end. Both the bars are having same diameter of 2 cm. The free ends of the Cu and the steel bars are maintained at $$100^\circ C$$ and $$0^\circ C$$ respectively. The curved surfaces of the bars are thermally insulated, what is the approximate temperature at Cu-steel junction?
(consider conductivity K of $$Cu = 400 J s^{-1} m^{-1} {^\circ C^{-1}}$$ and K for steel $$50 Js^{-1} m^{-1} {^\circ C^{-1}}$$)
A sample of gas ($$\gamma = 1.5$$) is taken through an adiabatic process in which the volume is compressed from 1600 cm$$^3$$ to 400 cm$$^3$$. If intial pressure is 150 kPa, then how muchwill be the final pressure in the process?
One mole of a monatomic gas is taken through a cycle ABCDA as shown in the P-V diagram. Column II give the characteristics involved in the cycle. Match the process $$A \rightarrow B$$ with the processes given in Column II.
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Process $$A \rightarrow B$$ signifies
Strain energy U, in the case of axially loaded bar is expressed as. (where P is axial load, L is bar length, A is cross-section area of the bar, E is Young’s Modulus of the bar, $$\sigma$$ is axial stress, $$\delta L$$ is elongation due to axial load)
Which of the following statements is correct, in case of a curved beam?
A Mohr’s circle reduces to a point when the body is subjected to
To drill holes of size 0.025mm, which is the most appropriate process?
Perforation in Aluminum plate occurs when it is connected with the Mild steel plate and exposed to the same environment. This phenomenon is explained by
A mixture of chemical compoundsor elements that have a single chemical composition and solidifies at the lowest temperature than any other composition made up of the same ingredients.
Which type of Gear meshing should be employed to transmit torque to a linear force?
