A point mass of 100 kg is dropped onto a massless elastic bar (cross-sectional area length = 1m, Young’s moduls = 100 GPa) from a height H of 10mm as shown (Figure is not to scale). If , the maximum compression of the elastic bar is _______ mm.

Question 2

Find the total extension in the stepped bar with an axial tensile load of 50 kN and having varying length of 2m, 3m, 5m and area of 200mm^{2}, 250mm^{2} and 300 mm^{2} as shown in given figure. E= 2×10^{5 }N/mm^{2} .

Question 3

The figure shows a state of plane stress. If the minimum principal stress is –7 MPa, then what is the value of σ_{x }?

Question 4

Two metal balls travelling at velocities v_{1} and v_{2} respectively collide with each other. Velocity of first ball before the impact was greater than second.

Considering it as a direct central impact, the velocities after the collision will be;

Question 5

A steel tube having outside and inside diameter of 100 mm and 60 mm respectively is bent in to the form of a quadrant of 2 m radius as shown in figure. The vertical deflection of the free under this load [Given E = 200 GPa]

Question 6

On an inclined plane the cylinder rolls down whose mass is 5Kg and radius 0.7m. determine the rotational kinetic energy when it reaches to foot of the plane if the height of inclined plane is 6m. take g=10m/s^{2}.

Question 7

Find the maximum value of in the situation shown in figure below so that the system remains at rest. Coefficient of friction at all surface of contact is. Pulley provided is smooth and tan

Question 8

The question has FOUR options. ONLY ONE of these four options is the correct answer

A constant force acting on a particle of mass 2kg is given by . What is the work done by given force during motion of particle from point A (1 m , 1 m, 0 m) to point B (3m, 4m, 2m)?

Question 9

A stone is dropped from a balloon going up with a uniform velocity of 10 m/s. if the balloon was 40 m high when the stone was dropped, the height of balloon from the ground when the stone hits the ground is (take g = 10 m/s^{2})

Question 10

The question has FOUR options. ONLY ONE of these four options is the correct answer.

The potential energy for a conservative system is given by

where a and b are positive constants.

Where is the equilibrium point situated?

Question 11

For the rod as shown in figure, the factor of safety according to maximum distortion energy theory is Assume S_{yt} = 200 MPa, S_{ut} = 400 MPa, μ = 0.3

Question 12

A uniform block weighing 500 kg is constrained by three wires. The tension in wire DB(in kg) will be

Question 13

The number of revolutions made by the wheel of a flywheel which increases its speed from 30 rpm to 60 rpm in 45 seconds are

Question 14

At point in a body stresses developed are such that σ_{x}= 140 MPa and σ_{y}= 60 MPa and the major principle stress is 150 MPa. What is the magnitude of max in-plane shear stress __________ (in MPa).

Question 15

The ratio of power transmission capacities of a solid and hollow circular shaft when they are rotating at the same rpm. Given that material, weight and length are same for both the shafts and k is the ratio of inner to outer diameter of the hollow shaft.

Question 16

The question has FOUR options. ONLY ONE of these four options is the correct answer.

A rigid body rotates about a fixed axis with variable angular velocity equal to α -βt at time t where α and β are constants. The angle through which it rotates before it comes to rest is

Question 17

The triangular shaped framed structure is

Question 18

Given blocks are acted by ∆T = 50ºC For steels, E_{s} = 200GPa , D_{s} = 75mm , α = 11.7 x 10^{-6} / ºC For copper , E_{c} = 70GPa , D_{s} = 50 mm , α = 21.6 x 10^{-6} / ºC

Find thermal stress on copper ___________?

Question 19

Match the following criteria of material failure, under biaxial stresses ï_{1} and ï_{2} and yield stress ï_{y}, with their corresponding graphic representations:

Question 20

A Hollow shaft of outer diameter 80 mm and inner diameter of 40 mm is to be replaced by a solid shaft to transmit the same torque at the same maximum stress. The diameter of solid shaft should be ____ mm.