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)

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 ]

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:

11.1 Measurements-01

Find the dimensions of

a.      Power

b.     Force

c.      Permittivity of free space

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 :

In LCR series circuit, an alternating e.m.f. ‘ e ’ and current ‘ i ’ is given by equation e = 100 sin ( 100 t ) and i = 100 sin [ 100 t + (π/3) ] mA The average power dissipated in the circuit will be _ _ _ _ _ _ _ _ _ ( MHT - CET 2014 )

a ) 100 W              b ) 10 W                      c ) 5 W                        d ) 2.5 W

Solution :

A planet of mass m moves in the inverse square central force field of the Sun of mass M . If the semi-major and semi-minor axes of the orbit are a and b , respectively, the total energy of the planet is:

          (a)    - ( G M m ) / ( a + b )

          (b)   - ( G M m ) [ ( 1 / a ) + ( 1 / b ) ]

          (c)    – [ ( G M m ) / a ] [ ( 1 / b ) - ( 1 / a ) ]

          (d)   - ( G M m ) / [ ( a – b ) / ( a + b )² ]

Consider three polarizer’s P1, P2 and P3 placed along an axis. The pass axis of P1 and P3 are at right angles to each other while the pass axis of P2 makes an angle θ with that of P1. A beam of unpolarized light of intensity I0 is incident on P1 as shown. The intensity of light emerging from P3 is

( a ) 0                                        ( b )   I ₀ / 2           

( c ) ( I ₀ / 8 ) sin ² 2 θ               ( d ) ( I ₀ / 4 ) sin ² 2 θ

Prove that the angle between the surface of an inclined plane and a the horizontal (the angle of inclination) is equal to the angle between the normal of the plane and the vertical.

 

The angle between the surface of an inclined plane and a the horizontal (the angle of inclination) is equal to the angle between the normal of the plane and the vertical.

Three particles, each having a charge of 10 µC are placed at corners of an equilateral triangle of side 10 cm. The electrostatic potential energy of system is ? ( Given 1/4πεo = 9 X 109 N-m2C2) (MHT-CET ~ 2011)

Three particles, each having a charge of 10 µC are placed at corners of an equilateral triangle of side 10 cm. The electrostatic potential energy of system is ? ( Given   = 9 X 10⁹ N-m²C²) (MHT-CET ~ 2011)

a ] zero                                 b] Infinity                            c] 27 J                    d] 100 J

Acceleration due to Gravity; The ratio of escape velocity.

The acceleration due to gravity ( g ) on the surface of the Earth is approximately 2 . 6 times that on the surface of the Mars . Given that the radius of Mars is about one half the radius of the Earth , the ratio of the escape velocity on Earth to that on Mars is approximately . . . . . . . . . . .

a ) 1 . 1
b ) 1 . 3
c ) 2 . 3
d ) 5 . 2