### Physics Solved Numericals For Class 11 | First Year | Karachi Board | AKUEB | In Urdu

## Chapter No.1 : The Scope of Physics (Watch)

1. Find the area of rectangular plate having length (21.3 +/- 0.2 ) cm and width (9.80 +/-0.10) cm.
2.Calculate (a) the circumference of circle of radius 3.5 cm. and (b) area of circle of radius 4.65 cm.
3.Prove that S=vit + 1/2 at^2 is correct dimensionally.
4.Suppose displace of a particle is related to a time according to a expression S= ct^3. what are the dimensions of constant c ?
5.Estimate the number of liters of gasoline used by all Pakistan's car each year.

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__Chapter No.2 : Scalars and Vectors __

6. the following forces act on a particle P: F1= 2i+3j-5k , F2=-5i+3j+5k , F3=i-2j+4k and F4=4i-3j-2k measured in newtons find (a) resultant of forces (b) the magnitude of the resultant force.
7. If A= 3i-j-4k , B=-2i+4j-3k and C=i +2j-k , find a) 2A-B+3C (b)|A + B +C | (c) |3A -2B +4C | (d) unit vector parallel to 3A -2B +4C
8.Two tug boats are towing a ship each exerts a force of 6000 N and the angle between the ropes is 60 degree.Calculate the resultant force on the ship.
9.The position vectors of point P and Q are given by r1= 2i + 3j – k , r2=4i-3j +2k. Determine PQ in terms of units vectors i ,j and k and find its magnitude.
10. Prove that the vectors A=3i+j-2k , B=-i + 3j +4k ,C=4i-2j-6k, can forms sides of triangle.Find the length of the medians of triangle.
11.Find the rectangular components of vector A, 15 units long when it forms angle with respect to +ve x axis of 50 degrees.
12.Two vectors 10 cm and 8 cm long form an angle of 60 degrees.Find the magnitude of difference and the angle with respect to the larger vector.
13.The angle between the vector A and B is 60 degrees.Given that |A|=|B|=1, calculate (a) |B- A| ;(b) |B + A|
14. A car weighing 10,000 N on a hill which makes an angle of 20 degrees with the horizontal. Find the components of car’s weight parallel and perpendicular to the road.

Q.15 Find the angle between A=2i + 2j – k and B=6i – 3j +2k.

Q.16 Find the projection of the vector A= i – 2j + k on to the direction of vector B=4i – 4j +7k

Q. 17 Find the angles alpha, beta and gamma which the vector A=3i – 6j +2k makes with the positive x,y,z axis respectively.

Q.18 Find the work done in moving an object along a vector r=3i – 2j +5k is the applied force is F=2i – j – k.

Q.19 Find the work done by a force 30,000 N in moving an object through a distance of 45 m when :(a) force is in the direction of motion;(b) force makes an angle of 40 degrees to the direction of motion.Find the rate at which the force is working at a time when the velocity is 2 m/s.

Q.20 Two vectors A and B such that |A|=3, |B|=4 and A. B=-5 , find
(a) The angle between A and B.
(b) The Length |A+B| and |A-B|
(c) The angle between (A+B) and (A-B)

Q.21 If A=2i-3j-k and B=i+4j-2k, Find
a)A x B , b) B x A ,c) (A+B) x (B-A)
Q.22 Determine the unit vector perpendicular to the plane A= 2i - 6j -3k and B= 4i +3j -k
Q.23 Using the definition of vector product,prove the law of sines for plane triangles of sides a, b and c.(a/sin A =b/ Sin B=c/ Sin C )
Q.24 If r1 and r2 are position (both lie in xy plane) making angles with positive x axis measured counter clockwise find their vector product when i) r1= 4cm and angle =30 and r2= 3m and angle =90 degrees.

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