GATE ME topic:mechanics PYQs & Answers — Page 37

Questions 361–370 of 1040. Imported answers require independent review unless marked reviewed.

Topic practice 1040 questionsPage 37 of 104

A cylindrical disc of mass

kg and radius

m was spinning at

rad/s when it was placed on a flat horizontal surface and released (refer to the figure). Gravity

acts vertically downwards as shown in the figure. The coefficient of friction between the disc and the surface is finite and positive. Disregarding any other dissipation except that due to friction between the disc and the surface, the horizontal velocity of the center of the disc, when it starts rolling without slipping, will be ________ m/s (round off to 2 decimal places).

Diagram for Mechanical Engineering question 51

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A rigid beam AD of length

m is hinged at frictionless pin joint A and supported by two strings as shown in the figure. String BC passes over two small frictionless pulleys of negligible radii. All the strings are made of the same material and have equal cross-sectional area. A force

kN is applied at C and the resulting stresses in the strings are within linear elastic limit. The self-weight of the beam is negligible with respect to the applied load. Assuming small deflections, the tension developed in the string at C is ________ kN (round off to 2 decimal places).

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A thin-walled cylindrical pressure vessel has mean wall thickness of

and nominal radius of

. The Poisson’s ratio of the wall material is 1/3. When it was subjected to some internal pressure, its nominal perimeter in the cylindrical portion increased by 0.1% and the corresponding wall thickness became

. The corresponding change in the wall thickness of the cylindrical portion, i.e.

, is ________ % (round off to 3 decimal places).

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In the configuration of the planar four-bar mechanism at a certain instant as shown in the figure, the angular velocity of the 2 cm long link is

rad/s. Given the dimensions as shown, the magnitude of the angular velocity

of the 4 cm long link is given by ____ rad/s (round off to 2 decimal places).

Diagram for Mechanical Engineering question 52

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A schematic of an epicyclic gear train is shown in the figure. The sun (gear 1) and planet (gear 2) are external, and the ring gear (gear 3) is internal. Gear 1, gear 3 and arm OP are pivoted to the ground at O. Gear 2 is carried on the arm OP via the pivot joint at P, and is in mesh with the other two gears. Gear 2 has 20 teeth and gear 3 has 80 teeth. If gear 1 is kept fixed at 0 rpm and gear 3 rotates at 900 rpm counter clockwise (ccw), the magnitude of angular velocity of arm OP is ________ rpm (in integer).

Diagram for Mechanical Engineering question 53

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A shaft AC rotating at a constant speed carries a thin pulley of radius

m at the end C which drives a belt. A motor is coupled at the end A of the shaft such that it applies a torque

about the shaft axis without causing any bending moment. The shaft is mounted on narrow frictionless bearings at A and B where AB = BC = L = 0.5 m. The taut and slack side tensions of the belt are

N and

N, respectively. The allowable shear stress for the material is 80 MPa. The self-weights of the pulley and the shaft are negligible. Use the value of

available in the on-screen virtual calculator. Neglecting shock and fatigue loading and assuming maximum shear stress theory, the minimum required shaft diameter is ______ mm (round off to 2 decimal places).

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Under orthogonal cutting condition, a turning operation is carried out on a metallic workpiece at a cutting speed of 4 m/s. The orthogonal rake angle of the cutting tool is 5°. The uncut chip thickness and width of cut are 0.2 mm and 3 mm, respectively. In this turning operation, the resultant friction angle and shear angle are 45° and 25°, respectively. If the dynamic yield shear strength of the workpiece material under this cutting condition is 100 MPa, then the cutting force is ____________ N (round off to one decimal place).

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A straight-teeth horizontal slab milling cutter is shown in the figure. It has 4 teeth and diameter (

) of 200 mm. The rotational speed of the cutter is 100 rpm and the linear feed given to the workpiece is 1000 mm/minute. The width of the workpiece (

) is 100 mm, and the entire width is milled in a single pass of the cutter. The cutting force/tooth is given by

, where specific cutting force

N/mm²,

is the width of cut, and

is the uncut chip thickness. The depth of cut (

) is

, and hence the assumption of

is invalid. The maximum cutting force required is ______ kN (round off to one decimal place).

Diagram for Mechanical Engineering question 54

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A 1 mm thick cylindrical tube, 100 mm in diameter, is orthogonally turned such that the entire wall thickness of the tube is cut in a single pass. The axial feed of the tool is 1 m/minute and the specific cutting energy (

) of the tube material is 6 J/mm

. Neglect contribution of feed force towards power. The power required to carry out this operation is ________ kW (round off to one decimal place).

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In an orthogonal machining operation, the cutting and thrust forces are equal in magnitude. The uncut chip thickness is 0.5 mm and the shear angle is 15°. The orthogonal rake angle of the tool is 0° and the width of cut is 2 mm. The workpiece material is perfectly plastic and its yield shear strength is 500 MPa. The cutting force is ________ N (round off to the nearest integer).

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GATE ME topic:mechanics PYQs

Question 51

Question 51

Question 52

Question 52

Question 53

Question 53

Question 54

Question 54

Question 55

Question 55