GATE ME Engineering Mechanics PYQs & Answers — Page 5

Questions 41–50 of 61. Imported answers require independent review unless marked reviewed.

A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of points P and R are

and

, in the x and y directions, respectively. The magnitude of the angular velocity of the body is

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The position vector

of point P (20, 10) is rotated anti-clockwise in X-Y plane by an angle

such that point P occupies position Q, as shown in the figure. The coordinates

of Q are

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(13.40, 22.32)

(22.32, 8.26)

(12.32, 18.66)

(18.66, 12.32)

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A block of mass 10 kg rests on a horizontal floor. The acceleration due to gravity is 9.81 m/s². The coefficient of static friction between the floor and the block is 0.2. A horizontal force of 10 N is applied on the block as shown in the figure. The magnitude of force of friction (in N) on the block is ______

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The figure shows an idealized plane truss. If a horizontal force of 300 N is applied at point A, then the magnitude of the force produced in member CD is ______ N.

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A car having weight

is moving in the direction as shown in the figure. The center of gravity (CG) of the car is located at height

from the ground, midway between the front and rear wheels. The distance between the front and rear wheels is

. The acceleration of the car is

, and acceleration due to gravity is

. The reactions on the front wheels (

) and rear wheels (

) are given by

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A ball of mass 3 kg moving with a velocity of 4 m/s undergoes a perfectly-elastic direct-central impact with a stationary ball of mass

. After the impact is over, the kinetic energy of the 3 kg ball is 6 J. The possible value(s) of

is/are

Your answerChoose one option.

1 kg only

6 kg only

1 kg, 6 kg

1 kg, 9 kg

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A truss is composed of members AB, BC, CD, AD and BD, as shown in the figure. A vertical load of 10 kN is applied at point D. The magnitude of force (in kN) in the member BC is

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A bar of uniform cross section and weighing 100 N is held horizontally using two massless and inextensible strings S1 and S2 as shown in the figure.

The tensions in the strings are

Your answerChoose one option.

T₁ = 100 N and T₂ = 0 N

T₁ = 0 N and T₂ = 100 N

T₁ = 75 N and T₂ = 25 N

T₁ = 25 N and T₂ = 75 N

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A ball is dropped from rest from a height of 1 m in a frictionless tube as shown in the figure. If the tube profile is approximated by two straight lines (ignoring the curved portion), the total distance travelled (in m) by the ball is ________ (correct to two decimal places).

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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 10 m/s

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

Your answerChoose one option.

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GATE ME Engineering Mechanics PYQs

Question 5

Question 16

Question 19

Question 20

Question 29

Question 29

Question 38

Question 5

Question 25

Question 28