1. What is unit vector? 2. State the principle of transmissibility. 3. State the general condition of equilibrium of a particle. 4. State Varignon’s theorem. 5. What is radius of gyration? 6. State principal axes of inertia. 7. State Newton’s law concerning equilibrium of particle. 8. What do you mean by impact of elastic bodies? 9. What is coloumb friction? 10. Define coefficient of Kinetic friction. 11. Define the following terms: (a) Coplanar forces (b) Concurrent forces. 12. State the necessary and sufficient conditions for static equilibrium of a particle in two dimensions. 13. Why the couple moment is said to be a free vector? 14. State the necessary and sufficient conditions for equilibrium of rigid bodies in two dimensions. 15. When will the product of inertia of a lamina become zero? 16. Write the SI units of the mass moment of inertia and of the area moment of inertia of a Lamina 17. A body moves along a straight line so that its displacement from a fixed point on the line is given by s = 3t2 + 2t. Find the velocity and acceleration at the end of 3 seconds. 18. A particle of mass 0 kg falls vertically from a height of 100 m from ground. What is the change in potential energy when it has reached a height of 50 m ? 19. State the laws of dry friction. 20. What is general plane motion? 21. When will centroid and center of mass coincides? 22. State D’Alembert’s principle? 23. A car runs with initial velocity of 30m/s. and uniform acceleration of 3m/s2. Find its velocity after 5 seconds. 24. When will the product of inertia of a lamina becomes zero? 25. List out the steps to be followed to draw the Free body diagram of a rigid body? 26. define polar moment of inertia of a lamina? 27. State the principle of work and Energy? 28. A rigid body rotates about fixed axis. Write the expression for angular velocity when the rotation is uniformly accelerated. 29. A stone is dropped from the top of a tower. It strikes the ground after 4 seconds. Find the height of the tower. 30. Define the polar moment of inertia? 1. (i) Distinguish between scalar and vector quantities. (ii) Forces R, S, T, U are collinear. Forces R and T act from left to right. Forces S and U act from right to left. Magnitudes of the forces R, S, T, U are 40 N, 45 N, 50 N and 55 N respectively. Find the resultant of R, S, T, U. 2. (i) State the parallelogram law of forces (ii) Find the magnitude and position of the resultant of the system of forces shown in Figure. 3 (i) State the polygon law of forces. (ii) A system of forces acts as shown in Figure. Find the magnitude of P and Q. so that the resultant of the force system passes through A and B. 4. (i) State the principle of moments. (ii) A rigid rod PQ is acted upon by a system of parallel forces as shown in Figure Find the equivalent single force for the given system of forces. Also find the equivalent force-moment system at A. Solve the problem using vector method. 5. (i) Define moment of inertia of a body. (ii) Find the moment of inertia of the section shown in Figure about the centroidal axes. (Dimensions in mm) 6. (i) Discuss radius of gyration of an area. (ii) Find the polar moment of inertia of a T section shown in Figure. about an axis passing through its centroid. Also find the radius of gyration with respect to the polar axis. (Dimensions in mm) 7. (i) What is impulsive force and impulsive motion? (ii) A block and pulley system is shown in Figure. The coefficient of kinetic friction between the block and the plane is 0.25. The pulley is frictionless. Find the acceleration of the blocks and the tension in the string when the system is just released. Also find the time required for 200 kg block to come down by 2 m. 8. (i) State the law of conservation of momentum. (ii) A block of mass 50 kg slides down a 35° incline and strikes a spring 1.5 m away from it as shown in Figure. The maximum compression of the spring is 300 mm when the block comes to rest. If the spring constant is 1 kN/m, find the coefficient of kinetic friction between the block and the plane. 9. (i) What is limiting friction? (ii) A pull of 250 N inclined at 30° to the horizontal plane is required just to move a body kept on a rough horizontal plane. But the push required just to move the body is 300 N. If the push is inclined at 30° to the horizontal, find the weight of the body and the coefficient of friction, and the coefficient of friction. 10. (i) State the factors influencing friction. (ii) Two blocks of weight 500 N and 900 N connected by a rod are kept on an inclined plane as shown in Figure. The rod is parallel to the plane. The coefficient of friction between 500 N block and the plane is 0.3 and that between 900 N block and the plane is 0.4. Find the inclination of the plane with the horizontal and the tension in the rod when the motion down the plane is just about to start. 11. (i) Determine the resultant of the concurrent force system shown in figure. (ii) Figure shows a 10 kg lamp supported by two cables AB and AC. Find the tension In each cable. 12. In the figure shown, three wires are joined at D. Two ends A and B are on the wall and the other end C is on the ground. The wire CD is vertical. A force of 60 kN is applied at 'D' and it passes through a point E on the ground as shown in ¯gure. Find the forces in all the three wires. 13. Two identical rollers, each of weight 500 N, are supported by an inclined plane making an angle of 30o to the horizontal and a vertical wall as shown in the figure. 14. (i) Sketch the free body diagrams of the two rollers. (ii) Assuming smooth surfaces, Find the reactions at the support points. 15. (i) Derive, from first principle, the second moments of area Ixx and Iyy for the rectangular area when the axes are as shown below: 16. Locate the centroid of the area shown in figure below. The dimensions are in mm. 17. (i) Explain the steps to be followed to find the principal moments of inertia of a given section. How will you find the inclination of the principal axes? (ii) A rectangular prism is shown in figure. The origin is at the geometric centre of the prism. The x, y and z-axes pass through the mid points of faces. 18. Derive the mass moment of inertia of the prism about the x-axis. 19, Two trains A and B leave the same station on parallel lines. A starts with a uniform acceleration of 0.15 m/s2 and attains the speed of 24 km/hour, after which, its speed remains constant. B leaves 40 seconds later with uniform acceleration of 0.30 m/s2 to attain a maximum speed of 48 km/hour. Its speed also becomes constant thereafter. When will B overtake A? 20. A ball of mass 2 kg, moving with a velocity of 3 m/s, impinges on a ball of mass 4 kg moving with a velocity of 1 m/s. The velocities of the two balls are parallel and inclined at 30± to the line of joining their centres at the instant of impact.
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