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GATE 2019: Engineering Mechanics Rapid Quiz-1 (App update required to attempt this test)

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Question 1

Three masses are connected to a rotating shaft supported on bearings A and B as shown in the figure. The system is in a space where the gravitational effect is absent. Neglect the mass of shaft and rods connecting the masses. For m1=10kg, m2=5kg and m3=2.5 kg and for a shaft angular speed of 1000 radian/s, the magnitude of the bearing reaction (in N) at location B is _____

Question 2

The rod PQ of length, and uniformly distributed mass of M=10 kg, is released from rest at the position shown in the figure. The ends slide along the frictionless faces OP and OQ. Assume acceleration due to gravity, g=10 m/s2. The mass moment of inertia of the rod about its centre of mass and an axis perpendicular to the plane of the figure is (ML2/12). At this instant, the magnitude of angular acceleration (in radian/s2) of the rod is _____

Question 3

The following figure shows the velocity-time plot for a particle travelling along a straight line. The displacement of the particle from t=0 to t=5s is ______ m.

Question 4

In a rigid body in plane motion, the point R is accelerating with respect to point P at If the instantaneous acceleration of point Q is zero, the acceleration (in m/s2) of point R is https://gs-post-images.grdp.co/2019/7/1-img1562060168251-85.PNG-rs-high-webp.PNG

Question 5

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 6

A point mass is shot vertically up from ground level with a velocity of 4 m/s at time, It loses 20% of its impact velocity after each collision with the ground. Assuming that the acceleration due to gravity is and that air resistance is negligible, the mass stops bouncing and comes to complete rest on the ground after a total time (in seconds) of

Question 7

The force in member AB is

Description: E:\Gate\SSC JE Mechanical Part 1\Made Easy Questions\10-RAC-Engg-Mechanics_BLok1_files\image041.jpg

Question 8

In the figure, the load P = 1 N, length L = 1 m, Young’s modulus E = 70 GPa, and the cross-section of the links is a square with dimension 10 mm × 10 mm. All joints are pin joints.

The stress (in Pa) in the link AB is ________ .
(Indicate compressive stress by a negative sign and tensile stress by a positive sign.)

Question 9

A rigid rod (AB. of length L = m is undergoing translational as well as rotational motion in the x-y plane (see the figure). The point A has the velocity V1 = i + 2j m/s. The end B is constrained to move only along the x direction.

The magnitude of the velocity V2 (in m/s) at the end B is____

Question 10

An object of mass m moving forward with velocity V along x-axis collides elastically with a stationary object Y of mass 2m at origin. After collision, the object X moves backward along x-axis. Given that the kinetic energy of the system is conserved, speed of object Y after collision is

Question 11

A particle of mass 1 kg moves in a straight line under the influence of a force which increases linearly with time at the rate of 60 N per second. At time t = 0, initial force may be taken as 50 N. Velocity of particle 4 sec after it started from rest at origin is __________ m/s.

Question 12

A reel of mass ‘m’ and radius of gyration ‘k’ is rolling down smoothly from rest with one end of the thread wound on it held in the ceiling as depicted in the figure. Consider the thickness of the thread and its mass negligible in comparison with radius ‘r’ of the hub and the reel mass ‘m’. Symbol ‘g’ represents the acceleration due to gravity.
Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE ME-28-Mar\GATE-ME-2003_files\image355.jpg
The linear acceleration of the reel is
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