F.Sc ICS Notes: Physics XI: Chapter 2 Vectors and Equilibrium Numerical Problems

F.Sc ICS Notes: Physics XI: Chapter 2 Vectors and Equilibrium Numerical Problems 1st Year Physics Notes Online Taleem Ilm Hub

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Numerical Problem 2.1: Suppose, in a rectangular coordinate system, a vector A has its tail at the point P(-2,-3) and its tip at Q(3,9). Determine the distance between these two points.
Numerical Problem 2.2: A certain corner of room is selected as the origin of a rectangular coordinate system. If an insect is sitting on an adjacent wall at a point having coordinate (2,1), where the units are in meters, what is the distance of insect from this corner of the room.
Numerical Problem 2.3: What is the unit vector in the direction of the vector A = 4i + 3j?
Numerical Problem 2.4: Two particles are located at r1 = 3i + 7j and r2 = -2i + 3j respectively. Find both the magnitude of the vector (r2,r1) and its orientation with respect to the x-axis.
Numerical Problem 2.5: If a vector B is added to vector A, the result is 6i + j. If B is subtracted from A the result is -4i + 7j. What is the magnitude of vector A?

Numerical Problem 2.6: Given that A = 2i + 3j and B = 3i - 4j, find the magnitude and distance of (a) C = A + B, and (b) D = 3A -2B.
Numerical Problem 2.7: Find the angle between the two vectors, A = 5i + j and B = 2i + 4j.

Numerical Problem 2.8: Find the work done when the point of application of the force 3i + 2j moves in a straight line from the point (2,-1) to the point (6,4).
Numerical Problem 2.9: Show that the three vector i + j +k, 2i - 3j + k and 4i + j - 5k are mutually perpendicular.
Numerical Problem 2.10: Given that A = i - 2j + 3k and B = 3i - 4k, find the length of the projection of A on B.

Numerical Problem 2.11: Vector A,B and C are 4 unit north, 3 units west and 6 unit east, respectively. Describe carefully (a) A x B (b) A x C (c) B x C.
Numerical Problem 2.12: The torque or turning effect of force about given point is given by r x F where r is the vector from the given point of application of F. Consider a force F = -3j + j + 5k acting on the point 7i +3j + k. What is the torque in Nm about the origin?
Numerical Problem 2.13: The line of force F = i - 2j passes through the point whose position vector is -j + k, Find (a) the moment of F about the origin, (b) the moment of F about the point of which the position vector is i + k.
Numerical Problem 2.14: The magnitude of dot and cross products to two vectors are value1 and value2 respectively. Find  the angle between the vectors.

Numerical Problem 2.15: A load of 10 N is suspended from a clothes line. This distorts the line so that it makes and angle of 15 with the horizontal at each end. Find the tension in the clothes line.

Numerical Problem 2.17: A spherical ball of weight 50 N is to be lifted over the step as shown in figure. Calculate the minimum force needed just to lift it above the floor.
Numerical Problem 2.18: A uniform sphere of weight 10 N is held by a string attached to a frictionless wall so that the string makes an angle of 30 with the wall as shown in figure. Find  the tension in the string and the force exerted on the sphere by the wall.

 Numerical Problem 2.16: A tractor of weight 15000 N crosses a single span bridge of weight 8000 N and of length 21.0 m. The bridge span is supported half a meter from either end. The tractor's front wheels take 1/3 of the total weight of the tractor, and the rear wheels are 3 m behind the front wheels. Calculate the force on the bridge supports when the rear wheels are at the middle of the bridge span.

Written By: Asad Hussain