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,

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(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.

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

The angle between vector ( i + j ) and ( j + k ) is ( in Radian )

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 :