A concentrated load is applied at the end of a cantilever as shown in Fig. The cross section of the beam is a square of side ‘a’ with a hole of dia ‘$$\frac{a}{2}$$’. The deflection at the tip of the cantilever is given by
ISRO Scientist or Engineer Mechanical 2013
For the following questions answer them individually
A cantilever beam is subjected to a UDL. The cross section of the beam is a H-Section placed as shownin Fig. The bendingstress distribution across the cross section will be
A thick cylinder of inner dia ‘D’, wall thickness $$t_2$$ and length ‘L’ is sealed at its both ends with caps. The thickness of the cap is $$t_1$$. Allowable tensile yield stress = $$\sigma_y$$ and allowable shear stress = $$\tau_y$$. A gas is pumped into this cylinder at pressure ‘p’. The cap will yield in shear at circumference of diameter ‘D’ when the gas pressure applied is more than
An ‘SS’ tube is inserted into an ‘Al' tube.They are permently fixed at one end .The other end is attached to a rigid plate .A torque "T" is applied to the rigid plate .A torque "T" is applied to the rigid plate .The circumference of the 'Al' tube at dia 'D' at the plate end with respect to the fixed end rotates by a distance ....mm due to the TORQUE 'T'.The polar MOI & rigidity modulus of Al & ss are $$J_{Al},G_{Al}$$ and $$J_{ss},G_{ss}$$ respectively
A rod of 20 dia is fixed to the ceiling of a roof on one end.: A rotor of 50 kg mass is attached to the free end with bearings. The CG of the rotor is 10 mm away from the shaft axis. The rotor is rotating at 600 rpm. The max tensile stress (in N/sq.mm)in the rod is nearly equal to
An automotive engine having a mass of 135 kg is supported on springs with linear characteristics. Each of the 2 front springs have stiffness of 3 $$\frac{MN}{m}$$ while the stiffness of each of 2 rear springs is 4.5 $$\frac{MN}{m}$$ The engine speed (rpm) at which resonanceis likely to occur is
A weighing $$\frac{m}{c}$$ consists of a 2 kg pan resting on a spring having linear characteristics. In this condition of resting on the spring, the length of spring is 200mm. Whena20 kg massis placed _on the pan,the length of the spring becomes 100mm. The undeformed length Lin mm and the spring stiffness K in $$\frac{N}{m}$$are
A circular shaft is subjected to a torque ‘T’ and a Bending Moment M. Theratio of max. shear stress to max. bendingstressis
A solid block ‘A’ wéighing ‘Q’ kg is resting on flat floor. A smooth cylinder ‘B’ weighing ‘P’ kg. is placed betweenthe solid A and the vertical wall as shownin fig. The friction between the cylinder, wail and the block A is negligible. The co-efficient of friction between the block A and floor is $$\mu$$ The minimum weight P required to disturb the block A is
A hydraulic jack is used to compress a spring as shown in the figure.Stiffness of spring is $$10^{5}$$ N/m By applying a pressure ‘p’ in the hydraulic cylinder, the spring gets compressed by 10 mm. The cross sectional area of the piston is 25 $$cm^{2}$$. The applied pressure‘p is
A small plastic boat loaded with pieces of steel rods is floating in a bath tub. If the cargo is , dumped in to the water, allowing the boatto float empty, the water level in the tub will
Viscosity of water in comparison to mercury is
Froude number is significant in:
The purpose of surge tank in pipeline is to
Head loss in turbulent flow in a pipe
A tank 1.5m stands on trolly and is full of water. It has an orifice of diameter 0.1m at 0.3m from the bottom of the tank. If the orifice is suddenly opened and coefficient of discharge of the orifice is 0.60, then the propelling force on the trolley will be
A modelof a hydraulic turbine is tested at a head of 1/4™ of that under which the full scale turbine works. The diameter of the modelis half of that of the full scale turbine. if N is the RPM of the full scale turbine, then RPM of the modelwill be
Consider steady, incompressible and irrotational flow through a reducer in a horizontal pipe, where the diameter is reduced from 20 cm to 10 cm. The pressure in the 20 cm pipe just upstream of the reduceris 150 kPa . The fluid has a vapour pressure of 50 kPa and a specific weight of 5 kN/m$$^3$$’. Neglecting frictional effects, the maximum discharge (in m$$^3$$/sec) that can pass through the reducer without causing cavitations is
For the stability of a floating body, under the influence of gravity alone, which of the following is true?
A smooth pipe of diameter 200mm carries water. The pressure in the pipe at Section $$S_{1}$$ (elevation: 10m) is 50 kPa _ At section $$S_{2}$$ (elevation: 12 m ) the pressure is 20 kPa and velocity is 2 $$\frac{m}{sec}$$. Density of water is 1000 $$\frac{kg}{m^{3}}$$ and acceleration due to gravity is 9.8 $$\frac{m}{sec}$$ ? . Which of the following is true?
The 2-D flow with velocity $$\overline{u} = (x + 2y + 2)1 + (4 - y)j$$ is
A venturimeter. of 20mm throat diameter is used to measure the velocity of water.in a horizontal pipe of 40mm diameter. If the pressure difference between the pipe and throat sections is found to be 30 kPa, then, neglecting frictional losses, the flow velocity is
A room contains 60 kg of air at 100 kPa and $$15^\circ$$C. The room has a 250-W refrigerator (the refrigerator consumes 250 W of electricity when running), a 120-W TV, a 1-kW electric resistance heater, and a 50-W fan. During a cold winter day,it is observed that the refrigerator, the TV, the fan, and the electric resistance heater are running continuously but the air temperature in the room remains constant. The rate of heat loss from the room that day is
Efficiency of Carnot engine is given as 80%. If the cycle direction is reversed, what will be the value of COP of reversed Carnotcycle
An adiabatic heat exchangeris used to heat cold water at $$15^\circ$$ C entering at a rate of 5 kg/s by hot air at $$90^\circ$$ C entering also at rate of 5 kg/s If the exit temperature of hot air is $$20^\circ$$ C, the exit temperature of cold water is
For given combined radiative and convective heat transfer coefficient ‘h;’ and given thermal conductivity kCritical thickness of insulation for cylinder and sphere is given as
Match the following
A spherical thermocouple junction of diameter 0.706 mm is to be used for the measurement of temperature of a gas streaim. The convective heat transfer co-efficient on the bead surface is 400 W/m$$^2$$K. Thermo-physical properties of thermocouple material are k = 20 W/mK , C = 400 J/kg K and r = 8500 kg/m$$^3$$ . If the thermocouple initially at $$30^\circ$$ C is placed in a hot stream of $$300^\circ$$ C, the time taken by the bead to reach $$298^\circ$$ C, is
Twoinsulating materials of thermal conductivity K and 2K are available for Jagging a pipe carrying a hotfluid. If the radial thickness of each material is the same.
The definition of 1 K as per the internationally accepted temperature scale is
Match the following
For a given heat flow and for the same thickness, the temperature drop across the material will be maximum for
Select statements from List II matching the processes in List I. Enter your answer as , B if the correct choice for (1) is (A) and that for (2) is (B)
In a radiative heat transfer, a gray surface is one
A system undergoes a state change from 1 to 2. According the second law of thermodynamicsfor the process to be feasible, the entropy change, S2 — S1 of the system
In descending order of magnitude, the thermal conductivity of (a) pure iron, (b) liquid water, (c) saturated water vapour and (d) aluminum can be arranged as
For the same inlet and outlet temperatures of hot and cold fluids, the Log Mean Temperature Difference (LMTD)is
A positive value of Joule-Thonison coefficient of a fluid means
A Carnot engine.rejects 30%of absorbed heat to a sink at $$30^\circ C$$. The temperature of the heat source is
An engine operates between temperaturelimits of 900 K and T and T and 400 K. For both to be equally efficient, the values of T will be
In a heat exchanger, the hot liquid enters with a temperature of $$180^\circ$$ and leaves at $$160^\circ$$ C. C. The cooling fluid enters at $$30^\circ$$C and leaves at $$110^\circ$$ C. The capacity ratio of the heat exchanger is
A system of massesrotating in different parallel planesis in dynamic balance if —
A torsion bar with a spring constant ‘k’ is cut into ‘n’ equal lengths. The spring constant for each portion would be
Logarithmic decrement of a dampedsingle degree of freedom system is 6. If stiffness of the spring is doubled and massis madehalf, then logarithmic decrementof the new
system will be equal to
To ensureself locking in a screw jackit is essential that helix angle is
For a particular load distribution and support condition in a beam of length “L, bending momentat any section ‘x’ (O <x <L)is given by $$M(x) = Ax-Bx^{2}$$, where A and B are constants. The shear force in the beam will be zero at ‘x’ equal to
If A is $$\begin{bmatrix}8 & 5 \\7 & 6 \end{bmatrix}$$ then $$\mid {A^{121}-A^{120}} \mid$$ is
If Ais Square Matrix of order 3, then product of A and its transpose is
The Matrix A=$$\begin{bmatrix}0 & -4 & 1 \\4 & 0 & -5 \\-1 & 5 & 0 \end{bmatrix}$$ is
Vector a= 3i + 2j — 6k, vector b= 4i — 3j + k, angle between abovevectorsis
If the probability for A to fail an examination is 0.2 and that for B is 0.3, then probability that either A of B fail is
Area bounded by the parabola 2y= $$x^{2}$$ and the line x=y-4 is equal to
Chancethat a leap year selected at random will contain 53 Sundays is
$$ \lim_{x \rightarrow 0} \frac{x{2} + x - \sin x}{x^{2}}$$
Two objects P & Q are traveling horizontally with velocity of 8 m/sec & 6 m/sec from left to right. They are separated by a distance of 15 m. The massof the objects are 3
kg and 5kg. lfthe coefficient of restitution is 0.7 what is the velocity $$(\frac{m}{s})$$ of P and Q after impact and when (seconds) and where (metres) will they impact with respect _to initial positioning of Q. The corresponding answersare respectively
The cross section of a compound bar 1 m long is as shown in figure. If the temperature is raised by $$80^\circ$$ C determine the stresses (in N/mm$$^2$$) in each metal
A short column of external diameter D and internal diameter d is subjected to a compressive load P acting with an eccentricity ‘e’. If the stresses at one of the extreme fiber is zero then the eccentricity has to be
The number of degrees of freedom in the 3 link mechanism shown below is given by
The equation of motion for a dampedvibrationis given by 6% + 9x+27x=0. The damping factor will be
A block brake with 400 mm diameter is used to brake a torque of 100 Nm as shown 60 in the figure. If the coefficient friction is 0.25 at the brake surface what is the value of force F to be applied at the end of the lever.
In the gear train of 1:10 as shown in the figure the pinion transmits 250 kw at 1800 rpm. What is the tangential load on the gear tooth
Spring back in nretal forming depends on
Which of the following processes induce morestress in the metal ?
The essential ingredient of any hardenedSteelis
Following is 2 process used to form powder metalto shape
A titanium sheet of 5.0 mm thickness is cut by wire-cut EDM process using a wire of 1.0 mm diameter. A uniform spark gap of 0.5 mm on bothsidesof the wire is maintained during
cutting operation.If the feed rate of the wire into the sheet is 20 mm/min, the material removal rate $$(in \frac{mm^{3}}{min})$$ will be
Diamondcutting tools are not recommended for machining of ferrous metals due to
Duringthe execution of a CNC part program block N020 G02 X45.0 Y25.0 R5.0 the type of tool motion will be
Projection Weldingis a
In a single point turning operation with a cemented carbide and steel combination having a Taylor exponentof 0.25,if the cutting speed is halved, then toollife will become
An oxidising process used for aluminium and magnesium articlesis called
Oneof the characteristics of Polymeris
Usually Materials with the following crystal structurefail in ductile mode
Work hardening strengthensan alloy by
An Aluminium object is made of a solid cone of height ‘h’ and base diameter D attached toa solid cylinder of diameter D and height ‘$$\frac{h}{2}$$’ as shown in figure. It is kept inclined touching to a vertical wall at point ‘A’ and hinged at. point B cr the floor. The object stays in this inclined position without going to vertical position (axis. perpendicular to the floor), only if. $$\theta$$ is less than
A hollow MSpipe is kept ona smoothstraight edge with the pipe mid pointsitting on it. A load “W’ Newtonsis applied at the ends which is keeping the pipe balanced in the horizontal condition. what is the safe maximum load ‘W’that can be applied withoutyielding the tube. Consider the self weight of the tube as ‘p’ $$\frac{N}{m}$$
Diameter of the pipe is 'd', Youngs modulus of pipe is E, Allowable yield stress is $$\sigma$$
A car crashes against a wall. Theinitial velocity at collision is 15$$\frac{m}{sec}$$ and the velocity after collision is 2.6$$\frac{m}{sec}$$ in the opposite direction. The massof the car is 1500kg. what is the average force exerted on the automobile bumperif collision lasts for 0.15 seconds.
Differential equation for the variation of amountof sait ‘x’ in a tank is given by :$$(\frac{dx}{dt} )+ (\frac{x}{20})$$ = 10. where x is in kg and t is in minutes. Assuming that at time zero thereis no salt in the tank, find the time at which the amountofsalt increases to 100kg
A5 mm diameter aluminium alloy test bar is subjected to a load of 560 N. if the diameterof the bar at this load is 4 mm,thetruestrain is
A material is dimensionally stable at room temperature if its glass transition temperature $$(T_{g})$$ is
