Understanding the Light Year: A Unit of Distance and Its Cosmic Significance

 Imagine you're gazing up at the night sky, marveling at the twinkling stars. Have you ever wondered how far away those stars are? What if I told you that the distances we measure in space are so vast that we use a special unit called a light year? In this blog post, we'll unravel the mystery of the light year, a fascinating unit of measurement that's pivotal in the field of astronomy.

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:

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

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.

CBSE AIPMT 2011

If power dissipated in 9 Ω resistor in a circuit shown is 36 watt the potential difference across 2 Ω resistance is

                       a)     8 V            

                       b)    10 V

                       c)     2V

                       d)    4 V

The equivalent magnetic moment of an electron revolving around a nucleus

An electron in an atom revolves around nucleus in an orbit of radius 0.5 Å. Calculate the equivalent magnetic moment, if the frequency of revolution of electron is 10¹⁰MHz

CBSE – AIPMT – 2011 de Broglie wavelength associated with electron

Electrons used in an electron microscope are accelerated by a voltage of 25 kV. If the voltage is increased to 100 km then the de-Broglie wavelength associated with the electrons would

(a) Increase by 4 times

(b) Increase by 2 times

(c) Decrease by 2 times

(d) Decrease by 4 times

JEE advance 2013 - A particle of mass 0.2 kg

A particle of mass 0.2 kg is moving in one dimension under a force that delivers a constant power 0.5 W to the particle. The initial speed (in m / s ) of the particle is zero, the speed ( in m / s ) after 5 sec is_ _ _ _ 

 { JEE advance 2013 }

The magnetic induction at center of coil

A Closely wound flat circular coil of 50 turns wound flat circular coil of 50 turns has a diameter of 10 cm carries a current of 4 ampere. Determine the magnetic induction at center of coil.

Solution:

A beam of Proton moves in a uniform magnetic field, the force acting on proton is______

A beam of proton ( q = 1.6 X 10 ^-19 C ) moves at 3 X 10 ⁵ m/s through a uniform magnetic field with magnitude 4 T, that is directed along Z axis. The velocity of each proton lies in X-Y plane at an angle 30^o to the Z axis. find the force on proton.

Solution :