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

**Suppose, in a rectangular coordinate system, a vector**

__Numerical Problem 2.1:__**A**has its tail at the point P(-2,-3) and its tip at Q(3,9). Determine the distance between these two points.

**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 2.2:__**What is the unit vector in the direction of the vector**

__Numerical Problem 2.3:__**A**= 4i + 3

*j?*

**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 2.4:__**If a vector B is added to vector**

__Numerical Problem 2.5:__**A**, the result is 6i + j. If

**B**is subtracted from

**A**the result is -4i + 7j. What is the magnitude of vector

**A**?

**Given that**

__Numerical Problem 2.6:__**A**= 2i + 3j and

**B**= 3i - 4j, find the magnitude and distance of (a)

**C**=

**A**+

**B**, and (b)

**D**= 3

**A**-2

**B**.

**Find the angle between the two vectors, A = 5i + j and B = 2i + 4j.**

__Numerical Problem 2.7:__**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 2.8:__**Show that the three vector i + j +k, 2i - 3j + k and 4i + j - 5k are mutually perpendicular.**

__Numerical Problem 2.9:__**Given that**

__Numerical Problem 2.10:__**A**= i - 2j + 3k and

**B**= 3i - 4k, find the length of the projection of

**A**on

**B**.

**Vector**

__Numerical Problem 2.11:__**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**.

**The torque or turning effect of force about given point is given by**

__Numerical Problem 2.12:__**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?

**The line of force**

__Numerical Problem 2.13:__**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.

__The magnitude of dot and cross products to two vectors are value1 and value2 respectively. Find the angle between the vectors.__

**Numerical Problem 2.14:**__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 2.15:**__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 2.17:**__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 2.18:**__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.__

**Numerical Problem 2.16:**
thank you so much! i was exactly looking for this.

ReplyDeleteAnswer to 2.16 question

ReplyDeleteR1+R2=15000+8000=23000

If we suppose left support as R1 and right support as R2

By taking moment about R1

R2×20=5000 (7)+8000 (10)+10000 (10)

Then R2= 10750=10.75kN by solving the above equation

By 1st equation

R1+R2=23000

Substitute the value of R2

Then R1=23000-10750=12.25kN