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?

Solution :

Given :

a)      q ₁ = 2 × 10 ^{– 7} C

b)      q ₂ = 3 × 10 ^{– 7} C

c)       r   = 30 cm = 30 X 10 ^{– 3} = 3 X 10 ^{– 2}

d)      ε ₀ = 8.854 × 10 ^{– 12} C ² N ^–1 m^{– 2}

Formula : 

The force between two small charged spheres can be given as

F = [ 1 / ( 4 π ε₀ ) ] [ ( q₁ q₂) / ( r² ) ]

Therefore,

F = [ 1 / ( 4 X 3.14 X 8.854 × 10^–12 ) ] { ( 2 × 10^–7 X 3 × 10^–7) / [ ( 3 X 10^{– 2})² ] }

F = [ 1/(1.11 × 10^–10 ) ] [ ( 6 × 10^–14 ) / ( 9 X 10 ^–4 ) ]

F = [ 9 X 10 ⁹ ) ] [ ( 6 × 10^–10 ) / ( 9 ) ]

F = 60 N

The force between two small charged spheres having charges of 2 × 10^–7C and 3 × 10^–7C placed 30 cm apart in air is 60 newton 

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 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 )

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 ]

केशवसुत स्मृती करंडक काव्यवाचन स्पर्धेत हरिभाई देसाई महाविद्यालयाचा संघ विजेता

GOLE AKSHAY CHANDRAKANT (AKSHAY GOLE)

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

जल है तो कल हैं

' एकूण ऋतू किती ? ' असा प्रश्न तुम्हाला विचारलात तर तुम्ही म्हणाल 'सोप्पंय !  तीन ऋतू आहेत , हिवाळा,  उन्हाळा आणि पावसाळा…… '  हे झाले पुस्तकी उत्तर, पण गेल्या चार ते पाच वर्षात झालेल्या वातावरणातील बदल पहिला तर आपल्या लक्षात येईल कि हे  ऋतूचक्रही बदलत चालले आहे.
                     

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.

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.

Two charges of equal magnitude q are placed in air at a distance 2 a apart and third charge -2q is placed at mid – point. The potential energy of a system is? ( ԑo = permittivity of free space ) . (MHT-CET ~ 2014)

Two charges of equal magnitude q are placed in air at a distance 2 a apart and third charge -2q is placed at mid – point. The potential energy of a system is? ( ԑ_o = permittivity of free space ) . (MHT-CET ~ 2014)

a ] - q ² / ( 8 π ε _o a )                        b] - 3 q ² / ( 8 π ε _o a )                     

c] – 5 q ² / ( 8 π ε _o a )                     d] - 7 q ² / ( 8 π ε _o a )

Two concentric sphere kept in air have radii R & r . they have similar change and equal charge density σ. The electric potential at their common centre is? ( MHT - CET ~ 2014 )

Two concentric sphere kept in air have radii R & r . they have similar change and equal charge density σ. The electric potential at their common centre is? ( MHT - CET ~ 2014 )

a ]  σ ( R + r ) / ε _o            b ] σ ( R – r ) / ε _o

c ] σ ( R + r ) / 2 ε _o               d ] σ ( R + r ) / 4 ε _o