General
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Physics-

A small particle of mass m blankis projected at an angle theta with the x-axis with an initial velocity v subscript 0 end subscript in the x-y plane as shown in the figure. A t blank a blank t i m e blank t less than fraction numerator v subscript 0 end subscript sin invisible function application theta over denominator g end fraction comma the angular momentum of the particle is

Physics-General

  1. negative m g v subscript 0 end subscript t to the power of 2 end exponent cos invisible function application theta blank stack stack j with dot on top with hat on top    
  2. negative fraction numerator 1 over denominator 2 end fraction m g v subscript 0 end subscript t to the power of 2 end exponent cos invisible function application theta blank stack k with hat on top    
  3. m g v subscript 0 end subscript t cos invisible function application theta blank stack k with hat on top    
  4. fraction numerator 1 over denominator 2 end fraction m g v subscript 0 end subscript t to the power of 2 end exponent cos invisible function application theta blank stack stack i with dot on top with hat on top    

    Answer:The correct answer is: negative fraction numerator 1 over denominator 2 end fraction m g v subscript 0 end subscript t to the power of 2 end exponent cos invisible function application theta blank stack k with hat on topL equals m open parentheses r cross times v close parentheses
    L equals m open square brackets v subscript 0 end subscript c o s theta blank t stack stack i with dot on top with hat on top plus open parentheses v subscript 0 end subscript s i n theta blank t minus fraction numerator 1 over denominator 2 end fraction g t to the power of 2 end exponent close parentheses stack stack j with dot on top with hat on top close square brackets
    cross times open square brackets v subscript 0 end subscript c o s theta blank stack stack i with dot on top with hat on top plus open parentheses v subscript 0 end subscript s i n theta minus g t close parentheses stack stack j with dot on top with hat on top close square brackets
    equals m v subscript 0 end subscript c o s theta blank t open square brackets negative fraction numerator 1 over denominator 2 end fraction g t close square brackets stack k with hat on top
    equals negative fraction numerator 1 over denominator 2 end fraction m g v subscript 0 end subscript t to the power of 2 end exponent c o s theta stack k with hat on top

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    General
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    A ray of light passes through an equilateral glass prism in such a manner that the angle of incidence is equal to the angle of emergence and each of these angles is equal to 3/4 of the angle of the prism. The angle of deviation is

    Is a band spectrum
    In the position of minimum deviation
    2 i equals A plus delta subscript m end subscript or delta subscript m end subscript equals 2 i minus A equals 90 minus 60 equals 3 0 to the power of o end exponent

    A ray of light passes through an equilateral glass prism in such a manner that the angle of incidence is equal to the angle of emergence and each of these angles is equal to 3/4 of the angle of the prism. The angle of deviation is

    physics-General
    Is a band spectrum
    In the position of minimum deviation
    2 i equals A plus delta subscript m end subscript or delta subscript m end subscript equals 2 i minus A equals 90 minus 60 equals 3 0 to the power of o end exponent
    General
    physics-

    A prism ABC of angle 30° has its face AC silvered. A ray of light incident at an angle of 45° at the face AB retraces its path after refraction at face AB and reflection at face AC. The refractive index of the material of the prism is

    A prism ABC of angle 30° has its face AC silvered. A ray of light incident at an angle of 45° at the face AB retraces its path after refraction at face AB and reflection at face AC. The refractive index of the material of the prism is

    physics-General
    General
    physics-

    A light ray is incident upon a prism in minimum deviation position and suffers a deviation of 34°. If the shaded half of the prism is knocked off, the ray will

    By formula delta equals left parenthesis n minus 1 right parenthesis A rightwards double arrow 34 equals left parenthesis n minus 1 right parenthesis A and in the second position delta to the power of ´ end exponent equals left parenthesis n minus 1 right parenthesis fraction numerator A over denominator 2 end fraction
    therefore fraction numerator 34 over denominator delta to the power of ´ end exponent end fraction equals fraction numerator left parenthesis n minus 1 right parenthesis A over denominator left parenthesis n minus 1 right parenthesis fraction numerator A over denominator 2 end fraction end fraction or delta to the power of ´ end exponent equals fraction numerator 34 over denominator 2 end fraction equals 1 7 to the power of o end exponent

    A light ray is incident upon a prism in minimum deviation position and suffers a deviation of 34°. If the shaded half of the prism is knocked off, the ray will

    physics-General
    By formula delta equals left parenthesis n minus 1 right parenthesis A rightwards double arrow 34 equals left parenthesis n minus 1 right parenthesis A and in the second position delta to the power of ´ end exponent equals left parenthesis n minus 1 right parenthesis fraction numerator A over denominator 2 end fraction
    therefore fraction numerator 34 over denominator delta to the power of ´ end exponent end fraction equals fraction numerator left parenthesis n minus 1 right parenthesis A over denominator left parenthesis n minus 1 right parenthesis fraction numerator A over denominator 2 end fraction end fraction or delta to the power of ´ end exponent equals fraction numerator 34 over denominator 2 end fraction equals 1 7 to the power of o end exponent
    General
    physics-

    A ray of monochromatic light is incident on one refracting face of a prism of angle 75 to the power of ring operator end exponent. It passes through the prism and is incident on the other face at the critical angle. If the refractive index of the material of the prism is square root of 2, the angle of incidence on the first face of the prism is

    From figure
    A equals r subscript 1 end subscript plus c equals r subscript 1 end subscript plus sin to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator mu end fraction close parentheses
    rightwards double arrow r subscript 1 end subscript equals 75 minus sin to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator mu end fraction close parentheses
    rightwards double arrow 75 minus 45 equals 3 0 to the power of o end exponent
    From Snell’s law At B
    mu equals fraction numerator sin invisible function application i over denominator sin invisible function application r subscript 1 end subscript end fraction rightwards double arrow square root of 2 equals fraction numerator sin invisible function application i over denominator sin invisible function application 3 0 to the power of o end exponent end fraction

    A ray of monochromatic light is incident on one refracting face of a prism of angle 75 to the power of ring operator end exponent. It passes through the prism and is incident on the other face at the critical angle. If the refractive index of the material of the prism is square root of 2, the angle of incidence on the first face of the prism is

    physics-General
    From figure
    A equals r subscript 1 end subscript plus c equals r subscript 1 end subscript plus sin to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator mu end fraction close parentheses
    rightwards double arrow r subscript 1 end subscript equals 75 minus sin to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator mu end fraction close parentheses
    rightwards double arrow 75 minus 45 equals 3 0 to the power of o end exponent
    From Snell’s law At B
    mu equals fraction numerator sin invisible function application i over denominator sin invisible function application r subscript 1 end subscript end fraction rightwards double arrow square root of 2 equals fraction numerator sin invisible function application i over denominator sin invisible function application 3 0 to the power of o end exponent end fraction
    General
    physics-

    The figures represent three cases of a ray passing through a prism of angle A. The case corresponding to minimum deviation is

    The figures represent three cases of a ray passing through a prism of angle A. The case corresponding to minimum deviation is

    physics-General
    General
    maths-

    If the normal at the point straight P left parenthesis theta right parenthesis to the ellipse x squared over 14 plus y squared over 5 equals 1 intersects it again at the point straight Q left parenthesis 2 theta right parenthesis, then cos space theta is

    If the normal at the point straight P left parenthesis theta right parenthesis to the ellipse x squared over 14 plus y squared over 5 equals 1 intersects it again at the point straight Q left parenthesis 2 theta right parenthesis, then cos space theta is

    maths-General
    General
    physics-

    A fighter plane enters inside the enemy territory, at time t equals 0 with velocity v subscript 0 end subscript equals 250 blank m s to the power of negative 1 end exponent and moves horizontally with constant acceleration a equals 20 m s to the power of negative 2 end exponent (see figure). An enemy tank at the border, spot the plane and fire shots at an angle theta equals 60 degree with the horizontal and with velocity u equals 600 blank m s to the power of negative 1 end exponent. At what altitude H of the plane it can be hit by the shot?

    If it is being hit then
    d equals v subscript 0 end subscript t plus fraction numerator 1 over denominator 2 end fraction a t to the power of 2 end exponent equals left parenthesis u cos invisible function application theta right parenthesis t
    or t equals fraction numerator u cos invisible function application theta minus v subscript 0 end subscript over denominator a divided by 2 end fraction

    therefore blank t equals fraction numerator 600 cross times fraction numerator 1 over denominator 2 end fraction minus 250 over denominator 10 end fraction equals 5 blank s
    H equals open parentheses u sin invisible function application theta close parentheses t minus fraction numerator 1 over denominator 2 end fraction cross times g t to the power of 2 end exponent
    equals 600 cross times fraction numerator square root of 3 over denominator 2 end fraction cross times 5 minus fraction numerator 1 over denominator 2 end fraction cross times 10 cross times 25
    H equals 2473 blank m

    A fighter plane enters inside the enemy territory, at time t equals 0 with velocity v subscript 0 end subscript equals 250 blank m s to the power of negative 1 end exponent and moves horizontally with constant acceleration a equals 20 m s to the power of negative 2 end exponent (see figure). An enemy tank at the border, spot the plane and fire shots at an angle theta equals 60 degree with the horizontal and with velocity u equals 600 blank m s to the power of negative 1 end exponent. At what altitude H of the plane it can be hit by the shot?

    physics-General
    If it is being hit then
    d equals v subscript 0 end subscript t plus fraction numerator 1 over denominator 2 end fraction a t to the power of 2 end exponent equals left parenthesis u cos invisible function application theta right parenthesis t
    or t equals fraction numerator u cos invisible function application theta minus v subscript 0 end subscript over denominator a divided by 2 end fraction

    therefore blank t equals fraction numerator 600 cross times fraction numerator 1 over denominator 2 end fraction minus 250 over denominator 10 end fraction equals 5 blank s
    H equals open parentheses u sin invisible function application theta close parentheses t minus fraction numerator 1 over denominator 2 end fraction cross times g t to the power of 2 end exponent
    equals 600 cross times fraction numerator square root of 3 over denominator 2 end fraction cross times 5 minus fraction numerator 1 over denominator 2 end fraction cross times 10 cross times 25
    H equals 2473 blank m
    General
    physics-

    A ray of light incident normally on an isosceles right angled prism travels as shown in the figure. The least value of the refractive index of the prism must be

    A ray of light incident normally on an isosceles right angled prism travels as shown in the figure. The least value of the refractive index of the prism must be

    physics-General
    General
    physics-

    Which of the following diagrams, shows correctly the dispersion of white light by a prism

    Because in dispersion of white light, the rays of different colours are not parallel to each other. Also deviation takes place in same direction.

    Which of the following diagrams, shows correctly the dispersion of white light by a prism

    physics-General
    Because in dispersion of white light, the rays of different colours are not parallel to each other. Also deviation takes place in same direction.
    General
    physics-

    A triangular prism of glass is shown in the figure. A ray incident normally to one face is totally reflected, if theta equals 4 5 to the power of o end exponent. The index of refraction of glass is

    For total internal reflection theta greater than C
    rightwards double arrow sin invisible function application theta greater than sin invisible function application C rightwards double arrow sin invisible function application theta greater than fraction numerator 1 over denominator mu end fraction
    or mu greater than fraction numerator 1 over denominator sin invisible function application theta end fraction rightwards double arrow mu greater than fraction numerator 1 over denominator sin invisible function application 4 5 to the power of o end exponent end fraction rightwards double arrow mu greater than square root of 2 rightwards double arrow mu greater than 1.41

    A triangular prism of glass is shown in the figure. A ray incident normally to one face is totally reflected, if theta equals 4 5 to the power of o end exponent. The index of refraction of glass is

    physics-General
    For total internal reflection theta greater than C
    rightwards double arrow sin invisible function application theta greater than sin invisible function application C rightwards double arrow sin invisible function application theta greater than fraction numerator 1 over denominator mu end fraction
    or mu greater than fraction numerator 1 over denominator sin invisible function application theta end fraction rightwards double arrow mu greater than fraction numerator 1 over denominator sin invisible function application 4 5 to the power of o end exponent end fraction rightwards double arrow mu greater than square root of 2 rightwards double arrow mu greater than 1.41
    General
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    A thin prism P subscript 1 end subscript with angle 6 to the power of ring operator end exponent and made from glass of refractive index 1.54 is combined with another thin prism P subscript 2 end subscript of refractive index 1.72 to produce dispersion without deviation. The angle of prism P subscript 2 end subscript will be

    fraction numerator A to the power of ´ end exponent over denominator A end fraction equals fraction numerator left parenthesis mu subscript y end subscript minus 1 right parenthesis over denominator left parenthesis mu subscript y ´ end subscript minus 1 right parenthesis end fraction rightwards double arrow fraction numerator A to the power of ´ end exponent over denominator 6 end fraction equals negative fraction numerator left parenthesis 1.54 minus 1 right parenthesis over denominator left parenthesis 1.72 minus 1 right parenthesis end fraction
    Þ A' equals negative 4.5 to the power of o end exponent equals 4 to the power of o end exponent 3 0 to the power of ´ end exponent

    A thin prism P subscript 1 end subscript with angle 6 to the power of ring operator end exponent and made from glass of refractive index 1.54 is combined with another thin prism P subscript 2 end subscript of refractive index 1.72 to produce dispersion without deviation. The angle of prism P subscript 2 end subscript will be

    physics-General
    fraction numerator A to the power of ´ end exponent over denominator A end fraction equals fraction numerator left parenthesis mu subscript y end subscript minus 1 right parenthesis over denominator left parenthesis mu subscript y ´ end subscript minus 1 right parenthesis end fraction rightwards double arrow fraction numerator A to the power of ´ end exponent over denominator 6 end fraction equals negative fraction numerator left parenthesis 1.54 minus 1 right parenthesis over denominator left parenthesis 1.72 minus 1 right parenthesis end fraction
    Þ A' equals negative 4.5 to the power of o end exponent equals 4 to the power of o end exponent 3 0 to the power of ´ end exponent
    General
    physics-

    A light ray is incident by grazing one of the face of a prism and after refraction ray does not emerge out, what should be the angle of prism while critical angle is C</em

    A light ray is incident by grazing one of the face of a prism and after refraction ray does not emerge out, what should be the angle of prism while critical angle is C</em

    physics-General
    General
    physics-

    A string of length L is fixed at one end and the string makes fraction numerator 2 over denominator pi end fraction rev/s around the vertical axis through, the fixed and as shown in the figure, then tension in the string is

    T sin invisible function application theta equals M omega to the power of 2 end exponent R (i)
    T sin invisible function application theta equals M omega to the power of 2 end exponent L blank s i n blank theta (ii)
    T equals M omega to the power of 2 end exponent L
    equals M bullet 4 pi to the power of 2 end exponent n to the power of 2 end exponent L
    equals M bullet 4 pi to the power of 2 end exponent open parentheses fraction numerator 2 over denominator pi end fraction close parentheses to the power of 2 end exponent L
    equals 16 blank M L

    A string of length L is fixed at one end and the string makes fraction numerator 2 over denominator pi end fraction rev/s around the vertical axis through, the fixed and as shown in the figure, then tension in the string is

    physics-General
    T sin invisible function application theta equals M omega to the power of 2 end exponent R (i)
    T sin invisible function application theta equals M omega to the power of 2 end exponent L blank s i n blank theta (ii)
    T equals M omega to the power of 2 end exponent L
    equals M bullet 4 pi to the power of 2 end exponent n to the power of 2 end exponent L
    equals M bullet 4 pi to the power of 2 end exponent open parentheses fraction numerator 2 over denominator pi end fraction close parentheses to the power of 2 end exponent L
    equals 16 blank M L
    General
    physics-

    A particle of mass m is rotating in a horizontal circle of radius R and is attached to a hanging mass M as shown in the figure. The speed of rotation required by the mass m keep M steady is

    To keep the mass M steady, let T is the tension in the string joining the two. Then for particle m comma
    T equals fraction numerator m v to the power of 2 end exponent over denominator R end fraction open parentheses i close parentheses
    For mass M comma
    T equals M g left parenthesis i i right parenthesis
    From Eqs. (i) and (ii)
    fraction numerator m v to the power of 2 end exponent over denominator R end fraction equals M g ⟹ v equals square root of fraction numerator M g R over denominator m end fraction end root

    A particle of mass m is rotating in a horizontal circle of radius R and is attached to a hanging mass M as shown in the figure. The speed of rotation required by the mass m keep M steady is

    physics-General
    To keep the mass M steady, let T is the tension in the string joining the two. Then for particle m comma
    T equals fraction numerator m v to the power of 2 end exponent over denominator R end fraction open parentheses i close parentheses
    For mass M comma
    T equals M g left parenthesis i i right parenthesis
    From Eqs. (i) and (ii)
    fraction numerator m v to the power of 2 end exponent over denominator R end fraction equals M g ⟹ v equals square root of fraction numerator M g R over denominator m end fraction end root
    General
    physics-

    Figure shows the variation of the stopping potential (V0) with the frequency (v) of theincident radiations for two different photosensitive material M1 and M2 .What are the values of work functions for M1 and M2 respectively

    Figure shows the variation of the stopping potential (V0) with the frequency (v) of theincident radiations for two different photosensitive material M1 and M2 .What are the values of work functions for M1 and M2 respectively

    physics-General