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 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:

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 :

The angle of minimum deviation of a glass prism is π – 2 A , where A is angle of prism. The angle of prism is _ _ _ _ _ _ _ _ _ _ _ _ .

    a )      2 tan μ

    b )      2 tan^-1 μ   

    c )       2 cot^-1 μ

    d )      2 cot μ

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 ]

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

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

solution :  -

Let us consider

A = i + j

B = j + k

To find out the