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GATE 2022 ME: Engineering Mechanics Revision Quiz

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Question 1

Three particles starts their motion from the origin at the same time, the first moves with a velocity u1 along the x-axis, the second moves along the y-axis with a velocity u2 and the third along the straight line y = x. Then, the velocity of the third particle so that all the three always lie on the same line is -

Question 2

For rolling condition, pick the correct option.

Question 3

A large number of bullets are fired in all directions with the same speed v from ground. What is the maximum area on the ground on which these bullets will spread (height of gun from ground assume negligible)-

Question 4

An aeroplane was flying horizontally with a velocity of 720 km/h at an altitude of 490 m. When it is just vertically above the target a bomb is dropped from it. How far (in m) horizontally it missed the target?

Question 5

A girl sits near the edge of a rotating circular platform. If the girl moves from circumference towards the centre of the platform then the angular velocity of the platform will-

Question 6

A uniform meter stick of mass M is hinged at one end and supported in a horizontal position by a string attached to the other end as shown in figure. If the string is cut, then the initial angular acceleration of the stick is-

Question 7

Two blocks connected by a massless string slide down an inclined plane having angle of inclination 37°. The masses of the two blocks are M1 = 4kg and M2 = 2kg respectively and the coefficients of friction 0.75 and 0.25 respectively. Which statement is correct.
(a) The common acceleration of the two masses is 1.3 ms–2
(b) The tension in the string is 14.7N
(c) The common acceleration of the two masses is 2.94 ms–2
(d) The tension in the string is 5.16N

Question 8

A simple structure ABCDE is supported on a hinge at A and on rollers at B while it carries a horizontal force of 1000 KN at E as shown in the figure.The magnitude of force (in KN) in member AC is _____.

Question 9

A stone of mass m is projected up with a velocity u reaches a maximum height H. When it is at a height of H/4 from the ground, the ratio of Kinetic Energy K and the potential energy P at that point is: (consider P = 0 at that point of projectory)

Question 10

A body is placed on a frictionless horizontal plane. The body is connected with an elastic spring which is initially unstretched. The plane is then gradually lifted from 0 º to 90 º then the curve between extension of spring Δl and angle of inclination θ is–

Question 11

A chain of length l is placed on a smooth spherical surface of radius r with one of its ends fixed at the top of the surface. Length of chain is assumed to be l < . Acceleration of each element of chain when upper end is released is–

Question 12

Figure shows a small wheel fixed coaxially on a bigger one of double the radius. The system rotates about the common axis. The strings supporting A and B do not slip on the wheels. If x and y be the distances travelled by A and B in the same time interval, then-

Question 13

In the figure, the blocks A, B and C of mass m each have accelerations a1, a2 and a3 respectively. F1 and F2 are external forces of magnitude 2mg and mg respectively. The mass of the block on which F2 is acting is m, same as the mass of block c.

Question 14

A particle is observed from two frames S1 and S2. The graph of relative velocity of S1 with respect to S2 is shown in figure. Let F1 and F2 be the pseudo forces on the particle when seen from S1 and S2 respectively. Which one of the following is not possible ?

Question 15

A pendulum of mass m and length η is suspended from the ceiling of a trolley which has a constant acceleration a in the horizontal direction as shown in figure. Work done by the tension is (In the frame of trolley) –
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