ESE ME Engineering Mechanics : National Champion Test for ESE & GATE ME Exams

Question 1

A car moving with speed u can be stopped in minimum distance x when brakes are applied. If the speed becomes n times, the minimum distance over which the car can be stopped would take the value

Question 2

A point mass is executing simple harmonic motion with amplitude of 10 mm and frequency of 4 Hz. The maximum acceleration (m/s²) of the mass is ______

Question 3

A block weighing 981 N is resting on a horizontal surface. The coefficient of friction between the block and the horizontal surface is μ = 0.2. A vertical cable attached to the block provides partial support as shown. A man can pull horizontally with a force of 100 N. What will be the tension, T (in N) in the cable if the man is just able to move the block to the right?

Question 4

A bullet spins as the shot is fired from a gun. For this purpose, two helical slots as shown in the figure are cut in the barrel. Projections A and B on the bullet engage in each of the slots.

Helical slots are such that one turn of helix is completed over a distance of 0.5 m. If velocity of bullet when it exits the barrel is 20 m/s, its spinning speed in rad/s is_________

Question 5

In a particle motion, which option describes the motion of particle A with reference to particle B?

Question 6

A circular object of radius r rolls without slipping on a horizontal level floor with the center having velocity V. The velocity at the point of contact between the object and the floor is

Question 7

An inextensible massless string goes over a frictionless pulley. Two weights of 100 N and 200 N are attached to the two ends of the string. The weights are released from rest, ad start moving due to gravity. The tension in the string (in N) is ____

Question 8

The degree of static indeterminacy of a rigid joined frame PQR supported as shown in the figure is

Question 9

For a linear elastic structural system, minimization of potential energy yields

Question 10

The symmetry of stress tensor at a point in the body under equilibrium is obtained from

Question 11

The components of strain tensor at a point in the plane strain case can be obtained by measuring longitudinal strain in following directions.

Question 12

A sign is required to be put up asking drivers to slow down to 30 km/h before entering zone Y (see figure). On this road, vehicles require 174 m to slow down to 30 kmn/h(the distance of 174 m includes the distance travelled during the perception reaction time of drivers). The sign can be read by 6/6 vision drivers from a distance of 48 m. The sign is placed at a distance of x m from the start of Zone Y so that even a 6/9 vision drive can slow down to 30 km/h before entering the zone. The minimum value of x is _______ m.

Question 13

An infinite soil slope with an inclination of 35 ° is subjected to seepage parallel to its surface. The soil has $Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\Civil Engg\Civil Engineeing-04-Apr\Civil-Engineering-2004_files\image186.png$ and $Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\Civil Engg\Civil Engineeing-04-Apr\Civil-Engineering-2004_files\image187.png$ . Using the concept of mobilized cohesion and friction, at a factor of safety of 1.5 with respect to shear strength, the mobilized friction angle is

Question 14

A particle moves along a curve whose parametric equations are : x=t³ + 2t, y=-3e^-2t and z = 2 sin (5t), where x, y and z show variations of the distance covered by the particle (in cm) with time t (in s). The magnitude of the acceleration of the particle (in cm/s²) at t = 0 is _________ cm²/s

Question 15

A cantiiever truss carries a concentrated load P as shown in the figure below:

What are the magnitudes of axial forces in the member I, II, and III, respectively?

Question 16

The force in member BC is

Question 17

The truss is shown in figure. The cross-sectional area of each member is ‘A’ and the modulus of elasticity of the material is uniformly E. The strain energy in the member XY is given by

Question 18

What is the force in the member BC of the plane frame shown below?

Question 19

What is the magnitude of the force in the membe BD in the figure given below?

Question 20

Two blocks with masses M and m are in contact with each other and are resting on a horizontal frictionless floor. When horizontal force is applied to the heavier, the blocks accelerate to the right. The force between the two blocks are