GATE XE discipline:engineering-sciences PYQs & Answers — Page 167

Questions 1661–1670 of 1772. Imported answers require independent review unless marked reviewed.

A rectangular sheet ABCD of dimensions

and

along X and Y directions, respectively, is stretched to a rectangle AB′C′D′, as shown. The maximum principal strain (

) and minimum principal strain (

) due to the stretch are given by

Diagram for Engineering Sciences question 64

Your answerChoose one option.

and

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A solid bar of uniform square cross-section of side

and length

is rigidly fixed to the supports at the two ends. When the temperature in the rod is increased uniformly by

, the bar undergoes elastic buckling. Assume Young’s modulus

and coefficient of thermal expansion

to be independent of temperature. The coefficient of thermal expansion

is given by

Your answerChoose one option.

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Two rigid blocks, of masses 10kg and 15kg, are arranged one on top of the other and placed on a horizontal rough surface as shown. The blocks are connected to each other through an inextensible cable passing over a frictionless pulley. The coefficients of static friction between the blocks and also between the bottom block and the surface are all equal to 0.3. The force

(in Newtons) needed to set the blocks in motion towards right is _________. (Assume acceleration due to gravity

Diagram for Engineering Sciences question 66

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A truss system EFGH shown below is built using members EF, GH and FH of the same cross-sectional area 10mm² and member FG of cross-sectional area 20mm². The total strain energy stored (in Nm) in the system due to a force

acting at F is __________. Assume elastic deformations and members are made of steel with elastic modulus of 200GPa.

Diagram for Engineering Sciences question 67

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A rigid frame grips on to a steel wall as shown using a powerful magnet at the top support G and with a roller support at E. EF is horizontal. A man stands on the platform attached to the frame 1m away from the wall as shown. Assume the frame and magnet assembly to be of negligible weight and the mass of the man to be 80kg. The magnitude of the reaction (in Newtons) exerted by the frame onto the steel wall due to the weight of the man is __________. The magnetic force of attraction of the magnet at no load condition is 1kN. Magnet can be assumed to be small enough that it offers negligible moment resistance. Assume acceleration due to gravity,

Diagram for Engineering Sciences question 68

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A manually operated band brake has a control lever EFG as shown and has a coefficient of kinetic friction equal to 0.2. The cylinder initially rotates clockwise at a constant frequency of 10 revolutions per second. A force P = 300N is applied at G. The pin support at O is frictionless. The radius of the cylinder is

and the radius of gyration is 0.1m. The mass of the cylinder is 50kg. Assume acceleration due to gravity

. The time required (in seconds) to reduce the rotational frequency to 5 revolutions per second is __________.

Diagram for Engineering Sciences question 69

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In a pin-connected mechanism shown, load P applied at F is 50N. Neglect the weight of the links and assume

for the spring. The bars EH and FG are pinned at O at their centre such that the lengths of EO, GO, HO and FO are all equal to

. The spring between G and H is unstretched when

. The angle

(in degrees) under equilibrium is __________.

Diagram for Engineering Sciences question 70

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The frame shown below carries a vertical load

at its free end D. The frame is fixed at A and has a roller support at B. Magnitude of the reaction force at B (in kN) is __________. Assume that the effect of the axial force on bending is negligible.

Diagram for Engineering Sciences question 71

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Consider the system shown below. Mass

is fixed to the rod AC at a distance

from the hinge point at B. Two springs of stiffness 3K and K are attached to the rod at points A and C, respectively. The natural frequency of angular oscillation of the system about B is 20 rad/s. Assume the rod to be rigid and massless. Magnitude of

(in metres) is __________. (

, and

Diagram for Engineering Sciences question 72

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The simply supported beam shown below is subjected to a clockwise moment

at point A and to counterclockwise moments

and

at points B and C, respectively. Which one of the following is the correct bending moment diagram (tensile at bottom is positive moment) for the beam?