List of top Mechanical Engineering Questions asked in Tamil Nadu Common Entrance Test

A bullet is fired upwards at an angle of \(30^\circ\) to the horizontal from a point P on a hill, and it strikes a target which is 80 m lower than P. The initial velocity of the bullet is 100 m/s. Calculate the maximum height to which the bullet will rise above the horizontal. Assume \( g = 9.81 \) m/s\(^2\).
The condition for a screw jack to be self-locking is that:
A reciprocating pump driven by a driving wheel is shown in the below figure. If the crank is 80 mm long and the connecting rod is 200 mm, determine the velocity of the piston in the position shown. The driving wheel rotates at 2000 rpm in the anticlockwise direction. 
reciprocating pump
A 5-kg uniform serving table is supported on each side by two pairs of identical links, AB and CD, and springs CE as shown in the below figure. If the bowl has a mass of 1 kg and is in equilibrium when \( \theta = 45^\circ \), determine the stiffness \( k \) of each spring. The springs are unstretched when \( \theta= 90^\circ \). Neglect the mass of the links. 
uniform serving table i
The gearing of a machine tool is shown in the below figure. The motor shaft is connected to gear A and rotates at 975 rpm. The gear wheels B, C, D, and E are fixed to parallel shafts rotating together. The final gear F is fixed on the output shaft. What is the speed of gear F? The number of teeth on each gear are as follows: \( A=20 \), \( B=50 \), \( C=25 \), \( D=75 \), \( E=26 \), and \( F=65 \). 
gearing of a machine tool
Currently, eighty-five percent of all neck injuries are caused by rear-end car collisions. To alleviate this problem, an automobile seat restraint has been developed that provides additional pressure contact with the cranium. During dynamic tests, the distribution of load on the cranium has been plotted and shown to be parabolic. Determine the equivalent resultant force and its location, measured from point A. 
neck injuries
A boiler drum consists of a cylindrical portion 4 m long, 1.5 m in diameter, and 2.25 cm thick. It is closed by hemispherical ends. In a hydraulic test to 6 MN/m\(^2\), how many liters of additional water will be pumped in after initial filling at atmospheric pressure? The hoop strain at the junction of the cylinder and hemisphere may be assumed to be the same for both.
Consider \( E = 200 \) GN/m\(^2\); for water, \( K = 2.13 \) GN/m\(^2\) and \( 1/m = 0.3 \).
A 6×19 wire rope with fiber core and tensile designation of 1570 is used to raise the load of 20 kN as shown in the below figure. The nominal diameter of the wire rope is 12 mm, and the sheave has 500 mm pitch diameter. Determine the expected life of the rope in years assuming 500 bends per week. 
wire rope with fiber core and tensile designation
A riveting machine is driven by a constant torque 3 kW motor. The moving parts including the flywheel are equivalent to 150 kg at 0.6 m radius. One riveting operation takes 1 second and absorbs 10000 N-m of energy. The speed of the flywheel is 300 r.p.m. before riveting. Find the speed immediately after riveting. How many rivets can be closed per minute?
An intermediate shaft of a gearbox, supporting two spur gears A and B and mounted between two bearings C1 and C2, is shown in the below figure. The pitch circle diameters of gears A and B are 500 and 250 mm respectively. The shaft is made of alloy steel 20MnCr5. (\( S_{ut} = 620 \) and \( S_{yt} = 480 \) N/mm\(^2\)). The factors \( k_b \) and \( k_t \) of the ASME code are 2 and 1.5 respectively. The gears are keyed to the shaft. Determine the shaft diameter using the ASME code. 
Intermediate shaft of a gearbox
The maximum pull in the tie rods of a turnbuckle used in the roof truss is 4.5kN. The tie rods are made of steel 40C8 ( 380 / ) 2 Syt = N mm and the factor of safety is 5. Determine the nominal diameter of the threads on the tie rod on the basis of maximum principal stress theory. Assume dc = 0.8d.
Calculate the matrix product \( C = AB \), where
\[A = \begin{bmatrix} 5 & 3 & 1 \\ 4 & 6 & 2 \\ 10 & 3 & 4 \end{bmatrix}, \quad B = \begin{bmatrix} 1 & 5 \\ 2 & 4 \\ 3 & 2 \end{bmatrix}\]
Which of the statements is not true for Bainite, which is a micro constituent in Iron–Carbon Alloys?
Identify the correct type of defect for casting shown below: 
defect for casting
In a machining operation that approximates orthogonal cutting, the cutting tool has a rake angle of 10°. The chip thickness before the cut \(t_0 = 0.50\) mm and the chip thickness after the cut \(t_c = 1.125\) mm. The shear plane angle \(\phi\) is ——–––––––––.
Assuming \(\sin 10^\circ = 0.173\) and \(\cos 10^\circ = 0.984\).
Identify the operation related to drilling which is illustrated in Figure below.
operation related to drilling
Which is the correct type of configuration of a CMM from the figure presented below? 
configuration of a CMM
The following options represent the work done (W) and heat transfer (Q) relations for the various thermodynamic processes. Identify the INCORRECT option.
[Consider \( c_v, c_p \) - specific heats at constant volume and constant pressure respectively, \( p \)- pressure, \( v, v_1, v_2 \) - specific volumes of working fluid, \( T_1, T_2 \) - temperature at starting and end of the process.]
All of the following options describe the availability and unavailable energy of a system EXCEPT:
Consider the indicator diagram for the heat engine as shown in the following figure. If the heat rejected by the engine to a heat sink is 1250 kJ/kg, the thermal efficiency (by considering one decimal place) of the engine is:
heat engine
A slab of 250 mm thick is made up of material ‘X’ and its thermal conductivity is 500 W/m·K. One of the surface is kept at 100°C and another surface is maintained at 25°C. The net heat flux across the surface is:
Consider the h-s diagram for the Rankine Cycle as shown in Figure. According to the h-s diagram, which of the following steady flow devices is responsible for process 3-4? 
Rankine Cycle
If \( k \) is the average height of irregularities and \( \delta \) is the thickness of the laminar sublayer, then the boundary is known to be hydrodynamically rough when:
If \( V \) is the velocity of fluid flow, \( V_1 \) and \( V_2 \) are velocity at inlet and outlet of the pipe, respectively, and \( k \) is the value of the coefficient depending on the fittings, then which of the following options has the correct match of case and loss of head?
A fluid jet discharges from 100 mm diameter nozzle and vena contracta formed has a diameter of 90 mm. If the coefficient of velocity is 0.95, then the coefficient of discharge of the nozzle is: