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GATE ME 2022: Engineering Mechanics

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Question 1

A block of mass m is placed on a surface with a vertical cross-section given by If coefficient of friction is 0.5, the maximum height above the ground at which block can be placed without slipping is

Question 2

A small block oscillates back and forth on a extremely smooth concave surface of radius 10 cm. The time period of small oscillations will be

Question 3

There is a car of mass m on a platform of mass M. The platform is kept on a smooth ice as shown in fig. If the car starts moving on the platform with a velocity V relative to platform then the velocity of platform recoil relative to ice is

Question 4

The correct free body diagram for the ladder shown in the figure is (both wall and floor rough)?

Question 5

A gun is mounted on a railroad car. The mass of the car, the gun, the shell, and operator is 100 kg, whereas mass of one shell is 10kg. If the velocity of the shell with respect to the gun (in its state before firing) is 300 m/s then the recoil speed of the car with respect to ground after the second shot is (neglect friction)

Question 6

Two vectors acting at 1300 when joined head to tail in anticlockwise direction have their resultant making an angle α to the first vector. The magnitude of the first vector is 50 units. If the resultant becomes perpendicular to the first vector then determine the value of the second vector(magnitude ).
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