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

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 }

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 ]

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.

Black Body Radiation

If the temperature of black body is increased by a factor of 2, the amount of energy and volume radiated increases by a factor of . . . . . . . . . .

( a ) 2               ( b ) 4               ( c ) 8               ( d ) 16

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