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ESE ME: Engineering Mechanics Champion Quiz 4

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Question 1

Two masses m are attached to opposite sides of a rigid rotating shaft in the vertical plane. Another pair of equal masses m₁ is attached to the opposite sides of the shaft in the vertical plane as shown in figure. Consider m = 1 kg, e = 50 mm, e₁ = 20 mm, b = 0.3 m, a = 2 m and a₁ = 2.5 m, For the system to be dynamically balanced, m₁ should be _____kg.

Question 2

A stone with mass of 0.1 kg is catapulted as shown in the figure. The total force F_x (in N) exerted by the rubber band as a function of distance x (in m) is given by F_x = 300x². If the stone is displaced by 0.1 m from the un-stretched position (x=0) of the rubber band, the energy stored in the rubber band is
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Question 3

A simple pendulum of length 5m, with a bob of mass 1 kg, is in simple harmonic motion. As it passes through its mean position, the bob has a speed of 5 m/s. the net force on the bob at the mean position is

Question 4

A steel wheel of 600 mm diameter rolls on a horizontal steel rail. It carries a load of 500 N. The coefficient of rolling resistance is 0.3. The force in N(passing through the centre), necessary to roll the wheel along the rail is

Question 5

A bullet of mass ‘m’ travels at a very high velocity v (as shown in the figure) and gets embedded inside the block of mass ‘M’ initially at rest on a rough horizontal floor. The block with the bullet is seen to move a distance ‘s’ along the floor. Assuming μ to be the coefficient to kinetic friction between the block and the floor and ‘g’ the acceleration due to gravity what is the velocity v of the bullet?
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Question 6

An annular disc has a mass m, inner radius R and outer radius 2R. The disc rolls on a flat surface without slipping. If the velocity of the center of mass is v, the kinetic energy of the disc is

Question 7

The assembly shown in the figure is composed of two massless rods of length l with two particles, each of mass m. the natural frequency of this assembly for small oscillations is

Question 8

Which among the following structure is not statically determinate?

Question 9

The figure shows a pair of pin jointed gripper tongs holding an object weighing 2000 N. the coefficient of friction ( $Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE ME 18-Mar\GATE-ME-2004_files\image158.png$ ) at the gripping surface is 0.1XX is the line of action of the input force and YY is the line of application of gripping force. If the pin joint is assumed to be frictionless, the magnitude of force F required to hold the weight is

Question 10

Two books of mass 1 kg each are kept on a table, one over the other. The coefficient of friction on every pair of contacting surfaces is 0.3. the lower book is pulled with a horizontal force F. the minimum value of F for which slip occurs between the two books is

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ESE & GATE ME Engineering Mechanics

Jun 19ESE & GATE ME