GATE XE kind:question PYQs & Answers — Page 81

Questions 801–810 of 1772. Imported answers require independent review unless marked reviewed.

A rectangular plate of uniform thickness having initial length

and width

is placed between two rigid immovable walls. The temperature of the plate is increased by

. The plate is free to expand along the

and

directions. The mid-surface of the plate remains in the

-plane. The Poisson’s ratio is

and the coefficient of thermal expansion is

. Assuming that the plate is initially free of stresses, the change in length of the plate after the increase in temperature is given by

Diagram for Engineering Sciences question 79

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A mass

kg is attached to a spring as shown in the figure. The coefficient of friction between the mass and the inclined plane is 0.25. Assume that the acceleration due to gravity is 10 m/s

and that static and kinetic friction coefficients are the same. Equilibrium of the mass is impossible if the spring force is

Diagram for Engineering Sciences question 80

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30 N

45 N

60 N

75 N

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The frame shown in the figure is subjected to a uniformly distributed load of 1000 N/m over a distance of 0.6 m. Neglecting the weight of the frame, the maximum shear force (in N) in the region between the supports

and

of the frame is

Diagram for Engineering Sciences question 81

______.

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A slider moving in a frictionless slot is connected with a linear spring

as shown in the figure. The following is known: stiffness of the spring = 2 kN/m, mass of the slider = 10 kg, and the unstretched length of the spring = 1 m. If the slider is released from rest at

the magnitude of its velocity (in m/s) when it passes through point

Diagram for Engineering Sciences question 82

is __________ (rounded off to the nearest integer)

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A sphere

of mass

is thrown into the air at 50 m/s along a direction

up from the horizontal. At the topmost point of its trajectory, it has a central (non-oblique) collision with another sphere

which is at rest on top of a vertical pole. Sphere

has a mass of

. Acceleration due to gravity is 10 m/s

. Neglect contact friction and air-resistance. If the coefficient of restitution is 0.3, then the speed (in m/s) of sphere

immediately after the collision is ________ (rounded off to one decimal place)

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The truck shown in the figure is moving on a horizontal road at a speed of 20 m/s. It is carrying a box of mass 100 kg, which is simply placed on the truck platform. The coefficient of friction between the truck platform and the box is 0.25. Take acceleration due to gravity as 10 m/s

. Assume uniform deceleration during braking, and the coefficients of static and kinetic friction to be the same. The shortest distance in meters in which the truck can be brought to rest without the box slipping is

Diagram for Engineering Sciences question 84

______(round off to the nearest integer)

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The stepped rod of length 2 m, shown in the figure, is fixed at both ends (A and C). The area of cross-section of portion AB is 200 mm

and that of portion BC is 100 mm

. Force

is applied at section B such that the section is displaced by 0.1 mm in the direction of the force. Young’s modulus of the rod is 200 GPa. The applied force

in N is

Diagram for Engineering Sciences question 85

______ (round off to the nearest integer)

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A cantilever beam has a span of 1 m and carries a uniformly distributed load of

N/m over a portion as shown. A force

N acts at a distance

from the fixed end. The distance

is such that the bending moment at the fixed end is zero. The beam has a rectangular cross-section of depth 20 mm and width 24 mm. For this loading, the magnitude of the maximum bending stress in the beam in MPa is

Diagram for Engineering Sciences question 86

______________ (round off to the nearest integer)

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The figure shows two identical mass-less beams AB and CD, each clamped at one of their ends. The left end of beam CD rests on the right end of beam AB such that the ends of the beams are just in contact. The beams are unstressed before the application of load. Assume no friction at the contact. Now, if a uniformly distributed load of 800 N/m is applied on beam CD, the bending moment at the end B of beam AB in N.m is __________ (rounded off to the nearest integer)

Diagram for Engineering Sciences question 87

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The energy equation for a reversible non-flow process can be expressed as

, where

is the heat transfer per unit mass,

is the internal energy per unit mass,

is the pressure, and

is the mass specific volume. This energy equation is not in exact differential form. It can be made exact differential by multiplying with the following integrating factor: (T is the absolute temperature)

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GATE XE kind:question PYQs

Question 79

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Question 88