PHE-04 BPHE-104 Mathematical Methods Solved Assignment 2018

Description

PHE-04/BPHE-104 Solved Assignment For IGNOU BSC 2018
Course Title: Mathematical Methods In Physics-I
This Solution Is Valid Till: 31st December 2018

Questions:

1. a) Calculate the volume of a parallelepiped whose sides are given by the vectors
§=3i+2j+12, B=—i+3j and E=2i+2j+512.

b) For a particle undergoing circular motion with an angular velocity 0) in a circle of radius r show that:

ω><((ω><r)=—ω²r
2. a) The position vector of an object is:

r=(1+t)^3/2 i+(1+ t)^3/2 j+t² k
Determine the angle between its velocity vector and acceleration vector at t = 0.

b) Determine the direction in which the scalar field φ(x, y) 2 xy2 + x3 y increases the
fastest at the point (1, 2).

3. a) Determine whether the following vector field is solenoidal, irrotational or both:
F=x²yi+xyzj—x²y²k
b) Show that for two scalar fields f and g:
∇x(f∇g)+∇x(g∇f)=0

4. a) Obtain the curl of the following vector field:
A=(é_r +rcosθé_θ+réφ)
b) Express the vector field F = xzi + (x² + y²)j+[x/z]k in cylindrical polar coordinates.

5. Calculate the work done by a force F = 2xi + 3 yj in moving a particle once counter—clockwise along the ellipse x²/4 + y² =1 . What do you understand from the answer?

6. Using Stokes’ Theorem evaluate the line integral {Edi where F = yi+ xz3 j – @2312
C

and Cis a circle x2 + y2 = 4 in the plane z = —3. (10)
a r

7. a) Show that V(lnr)=—2. (5)
r

b) Using Green’s Theorem evaluate the integral §C(y2dx+ 3xydy) where C is a semi

circle of radius 1 in the upper half plane, centered at the origin. (5)

8. a) A number is chosen at random from the first twenty five natural numbers. Calculate
the probability that the integer is divisible by 3 or 5. (5)

b) A random variable X has the following probability distribution:

0x2 for 0<x<3
f(X)=

0 otherwise
Determine the value of the constant c and Var (X). (5)

9. a) The probability that a student gets admission to a prestigious college is 0.3. If 5
students from the same school apply, what is the probability that at most 2 are
accepted? (5)

b) If three persons, on an average, come to a company for job interview per day, then
determine the probability that less than three people have come for an interview on
a given day. (5)

10. The variation of the specific heat capacity of air with temperature is given in the
following set of data:

Heat Capacity
(in k] kg’l K’l) 1.003 1.005 1.008 1.013 1.020 1.029

Temperature (in K) 250 300 350 400 450 500

Compute the correlation coefficient my. (10)

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