? rad/sec is the angular velocity of a crank whose radius is r. If it makes ?� w

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Question
ω rad/sec is the angular velocity of a crank whose radius is r. If it makes θ� with inner dead centre and obliquity of the connecting rod l is φ, the velocity v of the piston, is given by the equation
Options
A. ω²(l cos φ + r sin φ tan θ)
B. ω²(l sin φ + r cos φ tan θ)
C. ω(l sin φ + r cos φ tan θ)
D. ω²(l sin φ - r cos θ tan φ).

Correct Answer

ω(l sin φ + r cos φ tan θ)

Applied Mechanics problems

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1. A heavy ladder resting on a floor and against a vertical wall may not be in equilibrium, if
Options
A. floor is smooth and the wall is rough
B. floor is rough and the wall is smooth
C. floor and wall both are smooth surfaces
D. floor and wall both are rough surfaces.

3. On a ladder resisting on a smooth ground and leaning against a rough vertical wall, the force of friction acts
Options
A. towards the wall at its upper end
B. away from the wall at its upper end
C. upwards at its upper end
D. downwards at its upper end
E. none of these.

5. A ball which is thrown upwards, returns to the ground describing a parabolic path during its flight
Options
A. vertical component of velocity remains constant
B. horizontal component of velocity remains constant
C. speed of the ball remains constant
D. kinetic energy of the ball remains constant.

7. Kinetic friction may be defined as
Options
A. friction force acting when the body is just about to move
B. friction force acting when the body is in motion
C. angle between normal reaction and resultant of normal reaction and limiting friction
D. ratio of limiting friction and normal reaction.

8. For a particle moving with a simple harrmonic motion, the frequency is
Options
A. directly proportional to periodic time
B. inversely proportional to periodic time
C. inversely proportional to its angular velocity
D. directly proportional to its angular velocity
E. none of these.

9. A stone is whirled in a vertical circle, the tension in the string, is maximum
Options
A. when the string is horizontal
B. when the stone is at the highest position
C. when the stone is at the lowest position
D. at all the positions.

10. From the circular plate of a diameter 6 cm is cut out a circular plate whose diameter is equal to radius of the plate. The c.g. of the remainder shifts from the original position through
Options
A. 0.25 cm
B. 0.50 cm
C. 0.75 cm
D. 1.00 cm.

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