testing basic concept in physics

Testing the Basic Concept Prepared by Dr. Abhijit Kar Gupta

e-mail: kg.abhi@gmail.com 1. Calculate the arithmetic mean and root-mean-square (rms) value of the four numbers

1,2, 3, 4. Which one is greater? 2. Sketch the behaviours of the following functions: xe , xe− , xxe− , 2x 3. The motion of a body falling from rest in a resistive medium is described by the equation:

BvAdtdv

−= , where A and B are constants. Show that the velocity at any time t is

given by ( )BteBAv −−= 1 . Show that the velocity becomes constant (terminal) after a

long time. Can you plot v against t ? 4. You are given a cube. If its each side is increased by 10% then what will be the percentage change in its volume? 5. If θ be the angle between two vectors A and B then show that the resultant vector C has the magnitude θcos222 ABBAC ++= . What is C if A and B are perpendicular to each other?

6. For a simple pendulum total energy =+ 22

21

21 kxmv constant. Prove that the time

period kmT π2= .

7. If the magnitude of velocity of a body is measured to be 8 m/s and 12 m/s at time 2 sec. and 4 sec. respectively then find out the average acceleration of the body during this time.

8. Newton’s law of Gravitation is 221

rmm

GF = . Find out the dimension of the universal

constant G . Find out a quantity from the above relation whose dimension is mass per unit length. 9. Are the two vector products )ˆˆ(ˆ jii ×× and jii ˆ)ˆˆ( ×× equal?

10. A wave is represented by 005.0

sin2 ty π= . Find out the amplitude, wavelength and

frequency of the wave. 11. Are the following quantities scalar or vector? (i) r⋅∇ , (ii) r×∇ , where r is a position vector.