Winner of Physics Champion Contest -2

Hi All

We receive lot of entries for the contest.Thanks all for the Response

Answer to the questions are
1. c
2.a
3.b,c
4.b
5.a

The winner of the contest is Indranil Chakraborty from Mussoorie, Uttarakhand
He will soon recieve the stationary Gift worth RS 200
Congratutlation!!!!!!!!!!!!!


Thanks to all for overwhelming response!!!!!

IITJEE PHYSICS:Current Electricity Part -I

Agenda: Summary of Current Electricity

Some basic point about Electricty
-A current flows along a metal or wire when battery is connected to it.
-Current in a wire is due to free electrons moving along the wire
-The Battery has a Potential difference between its poles due to chemical changes inside the battery.The Potential difference pushes the electrons alongs the metal.The Potential diffrence between the terminal is call the EMF of the battery.
-One pole of the battery is called positive pole and another one is call the negative pole.
-Current direction is opposite to the electron flow direction.
-EMF is measured in Volt



Electric current is defined as the rate at which charge flows inside the conductor
so
I=Q/t
- Its unit is Amphere
Also I=dQ/dt

Drift speed of electrons inside the conductor
v_d=I/neA
Where I is the current,n is the number of the electron per unit volume ,e is the electronic charge and A is the area of the crossection of the conductor

Ohms Law

V=IR
where V is the Potential difference accross its ends
I is the current flow
And R is the electrical Resistance of the conductor.Electrical Resistance unit is Ohm


ELectrical Resistivity

It is defined as
ρ=RA/L

Where R is the Resistance
A is the crossectional Area
L is the length


Series Resistors

R=R₁+R₂+R₃

Parallel Resistors

(1/R)=(1/R₁)+(1/R₂)+(1/R₂)


Terminal Voltage of the Cell

V=E-Ir

where E is the EMF of the cell and r is the internal resistance of the Cell


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Physics for IITJEE:Exercise your Brain with Miscellaneous Physics Question

Question 1:
A 2 kg body moving to the right with speed 6 m/s coliides elastcally with a stationary body of mass 4 kg.
a.Find the velocity vector of each mass relative to center of mass before and after the collsion
b.Find the velocity vector of the each mass in original frame after the collision
c.How much energy was transfered to the 4 kg body.

Take i as the unit vector in the right direction

Answer
a.
Before collision
Velocity vector of mass 2 kg=4i m/s
Velocity vector of mass 4 kg=-2i m/s

After collision
Velocity vector of mass 2 kg=-4i m/s
Velocity vector of mass 4 kg=2i m/s

b
Velocity vector of mass 2 kg=-2i m/s
Velocity vector of mass 4 kg=4i m/s

c. 32 J

Hints:
Velocity of the center of mass=m₁v₁+m₂v₂/m₁+m₂
Velocity w.r.t CM=v-v_cm

Applying law of linear momentum and energy conservation,veloclities after collosion could be find out


Question 2:
A small solid cylinder of radius r rolls down from the top of sphere of Radius R without slipping.
a. find the angle made from the vertical at which the cylinder loses contact with the surface of the sphere
b.find the angular velocity of the cylinder at the moment it loses contact with the surface of the sphere

Answer
a. cos^-1(4/7)
b.(2/r)[(R+r)g/7]^1/2

hints:

Normal reaction will become zero at the point of losing contact
so centripetal force will become equal to the weight components across the radius.
Also applying law of conservation of energy ...we can find the solution


Question 3:

An gas obeys Vander waal equation

(P+a/V²)(V-b)=nRT

Find following for such a gas

A. The dimensional formula for constant a is
a.ML⁵T^-2
b.ML⁵T^-1
c.ML^-1T^-1
d. M⁰L^-0T⁰


B. Find the workdone by this gas when gas expand from V to 2V at constant temperature T
a.nRTlog_e(2V-b/V-b) -a/V
b.nRTlog_e(2V-b/V-b) +a/V
c. nRTlog_e(2V-b/V-b)
d. none of the above

C.Bulk modulus at constant pressure is defined as
K=(-1/V)(dP/dV)_T
Find the value of k for this gas
a.(1-b/V)(p-a/V²+2a/V³)
b. (1+b/V)(p-a/V²+2a/V³)
c.(1-b/V)(p-a/V²-2a/V³)
d.None of the above

Answer:
A.ML⁵T^-2
B.nRTlog_e(2V-b/V-b) -a/V



Question 4:
An electron (mass m and charge e) is moving along the axis of the ring of radius r and carrying a charge q.Find the time period of small oscillation of the electron about the center of the ring

Answer
T=4π(πε₀mr³/eq)^1/2

Hint:
Electric field at a point on the axis of the ring at the distance x from its center is
E=qx/4πε₀(r²+x²)^3/2