The Secret Double Life of Light: Why Scientists Fought for 200 Years!

 

Listen, between you and me, I know you sometimes act like you understand what I’m saying just to keep me motivated. It’s okay! But today, I’m going to let you in on a secret that is so strange, it made the smartest people in history act like grumpy toddlers.

For hundreds of years, the world of science was stuck in a "Cold War." On one side, you had the "Uncle Scientists" (the old school) and on the other, the "New-age kids." They were fighting over one thing: What is light? Is it a tiny bouncy ball or a wiggly wave? As it turns out, light is an invisible superhero with a secret identity that would make Batman jealous.

12.8 Stationary waves - How to determine linear density of wire

1.   A sonometer wire of length 0.5 m is stretched by a weight of 5 kg. The fundamental frequency of vibration is 100 Hz. Determine the linear density of material of wire.

How to find angular acceleration - 02

The angular displacement of a particle is given by

𝜃= 〖5𝑡〗^3+〖10𝑡〗^2−2𝑡+3, where time ‘t’ is in second and 𝜃 is in rad. The angular acceleration of particle at

t = 3 sec

a) 90 𝑟𝑎𝑑 𝑠^(−2)                     b) 110 𝑟𝑎𝑑 𝑠^(−2) 

c) 100 𝑟𝑎𝑑 𝑠^(−2)                   d) 120 𝑟𝑎𝑑 𝑠^(−2)

How to find angular acceleration....

The angular displacement of a particle is given by

𝜃= 〖6𝑡〗^2−4𝑡+6, where time ‘t’ is in second and 𝜃 is in rad. The angular acceleration of particle at t = 4 sec

a) 6 𝑟𝑎𝑑 𝑠^(−2)                       b) 24 𝑟𝑎𝑑 𝑠^(−2) 

c) 12 𝑟𝑎𝑑 𝑠^(−2)                     d) 48 𝑟𝑎𝑑 𝑠^(−2)

The relation between time ‘t’ and distance ‘x’ is t=ax^2+bx

The relation between time ‘t’ and distance ‘x’ is t=ax^2+bx,   where ‘a’ and  ‘b’ are constant. The acceleration is…..

a.   -2abv^2         
b.     2bv^2           
c.   -2av^3             
d.    2av^2

Coefficient of static friction between coin and the turntable.

A coin is kept at a distance 10 cm from the center of turn table of radius 1 m just begin to slip, when the turn table rotate at a speed of 90 r.p.m. calculate the coefficient of static friction between the coin ant turn table.

Solution:

JEE MAINS 2013 Measurement

Let [ε_o] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length and T = time and A = electric current then,

Top of Form

(A) [ ε_o ] = [ M⁻¹ L⁻³ T⁴ A² ]                          

(B) [ ε _o] = [ M⁻¹ L² T⁻¹ A⁻² ]

(C) [ ε_o ] = [ M⁻¹ L² T⁻¹ A ]

(D) [ ε_o ] = [ M⁻¹ L⁻³ T² A ]

The two charges of magnitude 1 μC and 2 μC are separated by 10 cm from each other. At what point on the line joining the two charges is the electric field strength is zero.

Solution:

A car moves with a constant speed 60 km / hr for 1 km and 40 km / hr in next 1 km what is the average speed of car?

Solution :

Oscillations

The displacement of an oscillating particle is given by x = a sin ( ω t ) + b cos ( ω t ), where a and b are constant show that the motion of particle is S. H. M.

Solution:

12- 6 Surface Tension -1

Calculate the force required to take awaya flat circular plate of radius 0.01m from the surface of water. The surface tension of water is 0.075  N / m.

Solution:

11.5 Friction - 1

A 20 kg metal block is placed on horizontal surface. A block is just begin to slide when the horizontal force of 100 N is applied to it. Calculate the coefficient of static friction. If the coefficient of kinetic friction is 0.4, find the minimum force to maintain its uniform motion.

 

Solution:

12 - 06 Surface Tension - 01

Calculate the force required to take away a flat circular plate of radius 0.01 m from the surface of water. The surface tension of water is 0.075 N / m

11.1 Measurements-01

Find the dimensions of

a.      Power

b.     Force

c.      Permittivity of free space

12.5. Elasticity - 1

A wire of length 2 m and area of cross section 10^-4 m² is stretched by a load 102 kg. The wire will stretched by 0.1 cm

Calculate

a.     Longitudinal stress

b.     Longitudinal strain

c.      Young’s modulus of wire

11.2. Scalars and Vectors – ( 1 )

Two forces f₁ and f₂ of magnitude 5N each inclined each other at 60^o, act on a body. Find the resultant force acting on body.

12.4. Oscillations - 1

A particle is executing S.H.M. of amplitude 5 cm and period of 2 sec. Find the speed of particle at a point where its acceleration is half of its maximum value.

Calculate the angular velocity of disc

A circular disc of mass 10 kg and radius 0.2 m is set in to rotation about an axis passing through its centre and perpendicular to its plane by applying torque 10 Nm. Calculate the angular velocity of disc that it will attain at the end of 6 sec from the rest.

Solution 

2.1 Show that the critical velocity of a body revolving in a circular orbit very closed to the surface of planet of radius ‘ R ’ and mean density ρ is Vc = 2 R √ [ (G ρ π ) / 3 ]

                      

Solution- 

1.1 Calculate the angular velocity and linear velocity of a tip of minute hand of length 10 cm.

1.1         Calculate the angular velocity and linear velocity of a tip of minute hand of length 10 cm.