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GATE CE: Solid Mechanics Champion Quiz 1

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Question 1

A solid metal bar of the uniform sectional area throughout its length hangs vertically from its upper end.
Details of the bar are : Length = 6m, material density = 8 x 10-6 N/mm3 and E = 2 x 105 N/mm2. The total elongation of the bar  ____ ×10-5 mm?

Question 2

The bending Moment diagram for a beam is given below:

The shear force at sections aa' and bb' respectively are of the magnitude

Question 3

The following statements are related to bending to beams:
I. The slope of the bending moment diagram is equal to the shear force.
II. The slope of the shear force diagram is equal to the load intensity.
III. The slope of the curvature is equal to the flexural rotation.
IV. The second derivative of the deflection is equal to the curvature
The only FALSE statement is

Question 4

The value of modulus of elasticity for a material is 200 GN/m2 and Poisson’s ratio is 0.25. What is its modulus of rigidity?

Question 5

If G is the modulus of rigidity, E the modulus of elasticity and the Poisson’s ratio for a material, then what is the expression for G?

Question 6

A bar of 40 mm diameter and 400 mm length is subjected to an axial load of 100 kN. It elongates by 0.150 mm and the diameter decreases by 0.005 mm. What is the Poisson’s ratio of the material of the bar?

Question 7

The reaction of the beam at C is

Question 8

A metal bar of 10 mm diameter when subjected to a pull of 23.5 kN gave an elongation of 0.3 mm on a gauge length of 200 mm. The Young’s modulus of elasticity of the metal will nearly be

Question 9

A cantilever beam OP is connected to another beam PQ with a pin joint as shown in the figure. A load of 10 kN is applied at the and-point of PQ. The magnitude of bending moment (in kN-m) at fixed end 0 is
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Question 10

A metal rod of initial length Lo is subjected to a drawing process. The length of the rod at any instant is given by the expression, L(t)= Lo (1+t2) , where t is the time in minutes. The true strain rate (in min-1) at the end of one minute is ________.
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Jul 27ESE & GATE CE