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 :

What is the force between two small charged spheres having charges of 2 × 10–7C and 3 × 10–7C placed 30 cm apart in air?

A ray of monochromatic light is incident at angle ‘i’ on the surface of glass slab. If the angle of refraction ‘r’ is twice the angle of incidence, the angle of incidence is_ _ _ _ _ _ _ _ .

a)      i =  sin ^{- 1} ( μ / 2 )

b)      i = 2 cos ^{- 1} ( μ / 2 )

c)       i =  cos ^{- 1} ( μ / 2 )

d)      i = 2 sin ^{- 1} ( μ / 2 )

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 ]

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.