Physics-
General
Easy

Question

Trajectories of two projectiles are shown in figure. Let T subscript 1 end subscriptand T subscript 2 end subscript be the time periods and u subscript 1 end subscript and u subscript 2 blank end subscripttheir speeds of projection. Then

  1. T subscript 2 end subscript greater than T subscript 1 end subscript    
  2. T subscript 1 end subscript equals T subscript 2 end subscript    
  3. u subscript 1 end subscript greater than u subscript 2 end subscript    
  4. u subscript 1 end subscript less than u subscript 2 end subscript    

The correct answer is: u subscript 1 end subscript less than u subscript 2 end subscript


    Maximum height and time of flight depend on the vertical component of initial velocity
    H subscript 1 end subscript equals H subscript 2 end subscript rightwards double arrow u subscript y end subscript subscript 1 end subscript equals u subscript y end subscript subscript 2 end subscript
    Here T subscript 1 end subscript equals T subscript 2 end subscript
    Range R equals fraction numerator u to the power of 2 end exponent sin invisible function application 2 blank theta over denominator g end fraction equals fraction numerator 2 left parenthesis u sin invisible function application theta right parenthesis left parenthesis u cos invisible function application theta right parenthesis over denominator g end fraction
    equals fraction numerator 2 u subscript x end subscript u subscript y end subscript over denominator g end fraction
    R subscript 2 end subscript greater than R subscript 1 end subscript therefore u subscript x subscript 2 end subscript end subscript greater than u subscript x subscript 1 end subscript end subscript blank o r blank u subscript 2 end subscript greater than u subscript 1 end subscript

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    A body is projected up a smooth inclined plane with a velocity v subscript 0 end subscript from the point A as shown in figure. The angle of inclination is 45 degree and top B of the plane is connected to a well of diameter 40 m. If the body just manages to cross the well, what is the value of v subscript 0 end subscript? Length of the inclined plane is 20 square root of 2 m, and g equals 10 m s to the power of negative 2 end exponent

    Let v be the velocity acquired by the body at B which will be moving making an angle 45 degree with the horizontal direction. As the body just crosses the well so fraction numerator v to the power of 2 end exponent over denominator g end fraction equals 40
    or v to the power of 2 end exponent equals 40 g equals 40 cross times 10 equals 400
    or v equals 20 blank m s to the power of negative 1 end exponent
    Taking motion of the body from A to B along the inclined plane we have
    u equals v subscript 0 end subscript comma a equals negative g sin invisible function application 45 degree equals negative fraction numerator 10 over denominator square root of 2 end fraction m s to the power of negative 2 end exponent
    s equals 20 m comma v equals 20 m s to the power of negative 1 end exponent
    As v to the power of 2 end exponent equals u to the power of 2 end exponent plus 2 a s
    therefore blank 400 equals v subscript 0 end subscript superscript 2 end superscript plus 2 open parentheses negative fraction numerator 10 over denominator square root of 2 end fraction close parentheses cross times 20 square root of 2
    or v subscript 0 end subscript superscript 2 end superscript equals 400 plus 400 equals 800 or v equals 20 square root of 2 m s to the power of negative 1 end exponent

    A body is projected up a smooth inclined plane with a velocity v subscript 0 end subscript from the point A as shown in figure. The angle of inclination is 45 degree and top B of the plane is connected to a well of diameter 40 m. If the body just manages to cross the well, what is the value of v subscript 0 end subscript? Length of the inclined plane is 20 square root of 2 m, and g equals 10 m s to the power of negative 2 end exponent

    physics-General
    Let v be the velocity acquired by the body at B which will be moving making an angle 45 degree with the horizontal direction. As the body just crosses the well so fraction numerator v to the power of 2 end exponent over denominator g end fraction equals 40
    or v to the power of 2 end exponent equals 40 g equals 40 cross times 10 equals 400
    or v equals 20 blank m s to the power of negative 1 end exponent
    Taking motion of the body from A to B along the inclined plane we have
    u equals v subscript 0 end subscript comma a equals negative g sin invisible function application 45 degree equals negative fraction numerator 10 over denominator square root of 2 end fraction m s to the power of negative 2 end exponent
    s equals 20 m comma v equals 20 m s to the power of negative 1 end exponent
    As v to the power of 2 end exponent equals u to the power of 2 end exponent plus 2 a s
    therefore blank 400 equals v subscript 0 end subscript superscript 2 end superscript plus 2 open parentheses negative fraction numerator 10 over denominator square root of 2 end fraction close parentheses cross times 20 square root of 2
    or v subscript 0 end subscript superscript 2 end superscript equals 400 plus 400 equals 800 or v equals 20 square root of 2 m s to the power of negative 1 end exponent
    General
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    The equation of the circumcircle of the triangle formed by the lines y plus square root of 3 x equals 6 comma y minus square root of 3 x equals 6 and y=0 is

    The equation of the circumcircle of the triangle formed by the lines y plus square root of 3 x equals 6 comma y minus square root of 3 x equals 6 and y=0 is

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    Which of the substance A comma blank B or C has the highest specific heat? The temperature v s time graph is shown

    Substances having more specific heat take longer time to get heated to a higher temperature and longer time to get cooled.

    If we draw a line parallel to the time axis then it cuts the given graphs at three different points. Corresponding points on the times axis shows that
    t subscript C end subscript greater than t subscript B end subscript greater than t subscript A end subscript rightwards double arrow C subscript C end subscript greater than C subscript B end subscript greater than C subscript A end subscript

    Which of the substance A comma blank B or C has the highest specific heat? The temperature v s time graph is shown

    physics-General
    Substances having more specific heat take longer time to get heated to a higher temperature and longer time to get cooled.

    If we draw a line parallel to the time axis then it cuts the given graphs at three different points. Corresponding points on the times axis shows that
    t subscript C end subscript greater than t subscript B end subscript greater than t subscript A end subscript rightwards double arrow C subscript C end subscript greater than C subscript B end subscript greater than C subscript A end subscript
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    The figure shows a system of two concentric spheres of radii r subscript 1 end subscript and r subscript 2 end subscript and kept at temperatures T subscript 1 end subscript and T subscript 2 end subscript respectively. The radial rate of flow of heat in a substance between the two concentric spheres, is proportional to

    To measure the radial rate of heat flow, we have to go for integration technique as here the area of the surface through which heat will flow is not constant.

    Let us consider an element (spherical shell) of thickness dx and radius x as shown in figure. Let us first find the equivalent thermal resistance between inner and outer sphere.
    Resistance of shell=d R equals blank fraction numerator d x over denominator K cross times 4 pi x to the power of 2 end exponent end fraction
    open parentheses fraction numerator F r o m blank R equals fraction numerator l over denominator K A end fraction w h e r e comma over denominator K equals t h e r m a l blank c o n d u c t i v i t y end fraction close parentheses
    rightwards double arrow not stretchy integral d R equals R equals not stretchy integral subscript r subscript 1 end subscript end subscript superscript r subscript 2 end subscript end superscript fraction numerator d x over denominator 4 pi K x to the power of 2 blank end exponent end fraction
    = fraction numerator 1 over denominator 4 pi K end fraction open square brackets fraction numerator 1 over denominator r subscript 1 end subscript end fraction minus blank fraction numerator 1 over denominator r subscript 2 end subscript end fraction close square brackets equals blank fraction numerator r subscript 2 end subscript minus r subscript 1 end subscript over denominator 4 pi K left parenthesis r subscript 1 end subscript r subscript 2 end subscript right parenthesis end fraction
    Rate of heat flow = H
    = fraction numerator T subscript 1 end subscript minus T subscript 2 end subscript over denominator R end fraction
    = fraction numerator T subscript 1 end subscript minus T subscript 2 end subscript over denominator r subscript 2 end subscript minus r subscript 1 end subscript end fraction blank cross times 4 pi K open parentheses r subscript 1 end subscript r subscript 2 end subscript close parentheses
    proportional to fraction numerator r subscript 1 end subscript r subscript 2 end subscript over denominator r subscript 2 end subscript minus blank r subscript 1 end subscript end fraction

    The figure shows a system of two concentric spheres of radii r subscript 1 end subscript and r subscript 2 end subscript and kept at temperatures T subscript 1 end subscript and T subscript 2 end subscript respectively. The radial rate of flow of heat in a substance between the two concentric spheres, is proportional to

    physics-General
    To measure the radial rate of heat flow, we have to go for integration technique as here the area of the surface through which heat will flow is not constant.

    Let us consider an element (spherical shell) of thickness dx and radius x as shown in figure. Let us first find the equivalent thermal resistance between inner and outer sphere.
    Resistance of shell=d R equals blank fraction numerator d x over denominator K cross times 4 pi x to the power of 2 end exponent end fraction
    open parentheses fraction numerator F r o m blank R equals fraction numerator l over denominator K A end fraction w h e r e comma over denominator K equals t h e r m a l blank c o n d u c t i v i t y end fraction close parentheses
    rightwards double arrow not stretchy integral d R equals R equals not stretchy integral subscript r subscript 1 end subscript end subscript superscript r subscript 2 end subscript end superscript fraction numerator d x over denominator 4 pi K x to the power of 2 blank end exponent end fraction
    = fraction numerator 1 over denominator 4 pi K end fraction open square brackets fraction numerator 1 over denominator r subscript 1 end subscript end fraction minus blank fraction numerator 1 over denominator r subscript 2 end subscript end fraction close square brackets equals blank fraction numerator r subscript 2 end subscript minus r subscript 1 end subscript over denominator 4 pi K left parenthesis r subscript 1 end subscript r subscript 2 end subscript right parenthesis end fraction
    Rate of heat flow = H
    = fraction numerator T subscript 1 end subscript minus T subscript 2 end subscript over denominator R end fraction
    = fraction numerator T subscript 1 end subscript minus T subscript 2 end subscript over denominator r subscript 2 end subscript minus r subscript 1 end subscript end fraction blank cross times 4 pi K open parentheses r subscript 1 end subscript r subscript 2 end subscript close parentheses
    proportional to fraction numerator r subscript 1 end subscript r subscript 2 end subscript over denominator r subscript 2 end subscript minus blank r subscript 1 end subscript end fraction
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    If the line y = x + 3 meets the circle x squared plus y squared equals a squared at A and B, then equation of the circle on AB as diameter is

    If the line y = x + 3 meets the circle x squared plus y squared equals a squared at A and B, then equation of the circle on AB as diameter is

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    An electric lamp is fixed at the ceiling of a circular tunnel as shown is figure. What is the ratio the intensities of light at base A and a point B on the wall

    I subscript A end subscript equals fraction numerator L over denominator left parenthesis 2 r right parenthesis to the power of 2 end exponent end fraction and I subscript B end subscript equals fraction numerator L over denominator open parentheses r square root of 2 close parentheses to the power of 2 end exponent end fraction cos invisible function application theta
    equals fraction numerator L over denominator 2 r to the power of 2 end exponent end fraction. fraction numerator r over denominator r square root of 2 end fraction equals fraction numerator L over denominator 2 square root of 2   r to the power of 2 end exponent end fraction

    therefore fraction numerator I subscript A end subscript over denominator I subscript B end subscript end fraction equals fraction numerator 2 square root of 2 over denominator 4 end fraction equals fraction numerator 1 over denominator square root of 2 end fraction

    An electric lamp is fixed at the ceiling of a circular tunnel as shown is figure. What is the ratio the intensities of light at base A and a point B on the wall

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    I subscript A end subscript equals fraction numerator L over denominator left parenthesis 2 r right parenthesis to the power of 2 end exponent end fraction and I subscript B end subscript equals fraction numerator L over denominator open parentheses r square root of 2 close parentheses to the power of 2 end exponent end fraction cos invisible function application theta
    equals fraction numerator L over denominator 2 r to the power of 2 end exponent end fraction. fraction numerator r over denominator r square root of 2 end fraction equals fraction numerator L over denominator 2 square root of 2   r to the power of 2 end exponent end fraction

    therefore fraction numerator I subscript A end subscript over denominator I subscript B end subscript end fraction equals fraction numerator 2 square root of 2 over denominator 4 end fraction equals fraction numerator 1 over denominator square root of 2 end fraction
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    The distance between a point source of light and a screen which is 60 cm is increased to 180 cm. The intensity on the screen as compared with the original intensity will be

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    The distance between a point source of light and a screen which is 60 cm is increased to 180 cm. The intensity on the screen as compared with the original intensity will be

    physics-General
    I proportional to fraction numerator 1 over denominator r to the power of 2 end exponent end fraction rightwards double arrow fraction numerator I subscript 2 end subscript over denominator I subscript 1 end subscript end fraction equals fraction numerator r subscript 1 end subscript superscript 2 end superscript over denominator r subscript 2 end subscript superscript 2 end superscript end fraction equals fraction numerator 6 0 to the power of 2 end exponent over denominator 18 0 to the power of 2 end exponent end fraction equals fraction numerator 1 over denominator 9 end fraction
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    The pole of the straight line 9x + y – 28 = 0 with respect to the circle 2 x squared plus 2 y squared minus 3 x plus 5 y minus 7 equals 0 is

    The pole of the straight line 9x + y – 28 = 0 with respect to the circle 2 x squared plus 2 y squared minus 3 x plus 5 y minus 7 equals 0 is

    Maths-General
    General
    physics-

    Three rods of equal length l are joined to form an equilateral triangle P Q R. O is the mid point of P Q. Distance O R remains same for small change in temperature. Coefficient of linear expansion for P R and R Q is same, i. e. comma blank alpha subscript 2 end subscript but that for P Q is alpha subscript 1 end subscript. Then

    open parentheses O R close parentheses to the power of 2 end exponent equals open parentheses P R close parentheses to the power of 2 end exponent minus open parentheses P O close parentheses to the power of 2 end exponent equals l to the power of 2 end exponent minus open parentheses fraction numerator l over denominator 2 end fraction close parentheses to the power of 2 end exponent
    equals open square brackets l open parentheses 1 plus alpha subscript 2 end subscript t close parentheses close square brackets to the power of 2 end exponent minus open square brackets fraction numerator l over denominator 2 end fraction open parentheses 1 plus alpha subscript 1 end subscript t close parentheses close square brackets to the power of 2 end exponentl to the power of 2 end exponent minus fraction numerator l to the power of 2 end exponent over denominator 4 end fraction equals l to the power of 2 end exponent open parentheses 1 plus alpha subscript 2 end subscript superscript 2 end superscript t to the power of 2 end exponent plus 2 alpha subscript 2 end subscript t close parentheses minus fraction numerator l to the power of 2 end exponent over denominator 4 end fraction left parenthesis 1 plus alpha subscript 1 end subscript superscript 2 end superscript t to the power of 2 end exponent plus 2 alpha subscript 1 end subscript t right parenthesis
    Neglecting alpha subscript 2 end subscript superscript 2 end superscript t to the power of 2 end exponent and alpha subscript 1 end subscript superscript 2 end superscript t to the power of 2 end exponent
    0 equals l to the power of 2 end exponent open parentheses 2 alpha subscript 2 end subscript t close parentheses minus fraction numerator l to the power of 2 end exponent over denominator 4 end fraction open parentheses 2 alpha subscript 1 end subscript t close parentheses rightwards double arrow 2 alpha subscript 2 end subscript equals fraction numerator 2 alpha subscript 1 end subscript over denominator 4 end fraction rightwards double arrow alpha subscript 1 end subscript equals 4 alpha subscript 2 end subscript

    Three rods of equal length l are joined to form an equilateral triangle P Q R. O is the mid point of P Q. Distance O R remains same for small change in temperature. Coefficient of linear expansion for P R and R Q is same, i. e. comma blank alpha subscript 2 end subscript but that for P Q is alpha subscript 1 end subscript. Then

    physics-General
    open parentheses O R close parentheses to the power of 2 end exponent equals open parentheses P R close parentheses to the power of 2 end exponent minus open parentheses P O close parentheses to the power of 2 end exponent equals l to the power of 2 end exponent minus open parentheses fraction numerator l over denominator 2 end fraction close parentheses to the power of 2 end exponent
    equals open square brackets l open parentheses 1 plus alpha subscript 2 end subscript t close parentheses close square brackets to the power of 2 end exponent minus open square brackets fraction numerator l over denominator 2 end fraction open parentheses 1 plus alpha subscript 1 end subscript t close parentheses close square brackets to the power of 2 end exponentl to the power of 2 end exponent minus fraction numerator l to the power of 2 end exponent over denominator 4 end fraction equals l to the power of 2 end exponent open parentheses 1 plus alpha subscript 2 end subscript superscript 2 end superscript t to the power of 2 end exponent plus 2 alpha subscript 2 end subscript t close parentheses minus fraction numerator l to the power of 2 end exponent over denominator 4 end fraction left parenthesis 1 plus alpha subscript 1 end subscript superscript 2 end superscript t to the power of 2 end exponent plus 2 alpha subscript 1 end subscript t right parenthesis
    Neglecting alpha subscript 2 end subscript superscript 2 end superscript t to the power of 2 end exponent and alpha subscript 1 end subscript superscript 2 end superscript t to the power of 2 end exponent
    0 equals l to the power of 2 end exponent open parentheses 2 alpha subscript 2 end subscript t close parentheses minus fraction numerator l to the power of 2 end exponent over denominator 4 end fraction open parentheses 2 alpha subscript 1 end subscript t close parentheses rightwards double arrow 2 alpha subscript 2 end subscript equals fraction numerator 2 alpha subscript 1 end subscript over denominator 4 end fraction rightwards double arrow alpha subscript 1 end subscript equals 4 alpha subscript 2 end subscript
    General
    physics-

    A point source causes photoelectric effect from a small metal plate Which of the following curves may represent the saturation photocurrent as a function of the distance between the source and the metal?

    A point source causes photoelectric effect from a small metal plate Which of the following curves may represent the saturation photocurrent as a function of the distance between the source and the metal?

    physics-General
    General
    physics-

    One of the following figures respesents the variation of particle momentum with associated de Broglie wavelength
    a)
    b)
    c)

    One of the following figures respesents the variation of particle momentum with associated de Broglie wavelength
    a)
    b)
    c)

    physics-General
    General
    physics-

    Two circular discs A and B with equal radii are blackened. They are heated to some temperature and are cooled under identical conditions. What inference do you draw from their cooling curves?

    According to Newton’s law of cooling, rate of cooling is given by
    open parentheses fraction numerator negative d T over denominator d t end fraction close parentheses equals fraction numerator e A sigma over denominator m c end fraction left parenthesis T to the power of 4 end exponent minus T subscript 0 end subscript superscript 4 end superscript right parenthesis
    Where c is specific heat of material.
    or open parentheses fraction numerator negative d T over denominator d t end fraction close parentheses proportional to fraction numerator 1 over denominator c end fraction
    i e. comma blankrate of cooling varies inversely as specific heat. From the graph, for A rate of cooling is larger. Therefore, specific heat of A is smaller.

    Two circular discs A and B with equal radii are blackened. They are heated to some temperature and are cooled under identical conditions. What inference do you draw from their cooling curves?

    physics-General
    According to Newton’s law of cooling, rate of cooling is given by
    open parentheses fraction numerator negative d T over denominator d t end fraction close parentheses equals fraction numerator e A sigma over denominator m c end fraction left parenthesis T to the power of 4 end exponent minus T subscript 0 end subscript superscript 4 end superscript right parenthesis
    Where c is specific heat of material.
    or open parentheses fraction numerator negative d T over denominator d t end fraction close parentheses proportional to fraction numerator 1 over denominator c end fraction
    i e. comma blankrate of cooling varies inversely as specific heat. From the graph, for A rate of cooling is larger. Therefore, specific heat of A is smaller.
    General
    physics-

    Which of the curves in figure represents the relation between Celsius and Fahrenheit temperatures

    fraction numerator C over denominator 5 end fraction equals fraction numerator F minus 32 over denominator 9 end fraction rightwards double arrow C equals open parentheses fraction numerator 5 over denominator 9 end fraction close parentheses F minus fraction numerator 20 over denominator 3 end fraction. Hence graph between ℃ and ℉ will be a straight line with positive slope and negative intercept

    Which of the curves in figure represents the relation between Celsius and Fahrenheit temperatures

    physics-General
    fraction numerator C over denominator 5 end fraction equals fraction numerator F minus 32 over denominator 9 end fraction rightwards double arrow C equals open parentheses fraction numerator 5 over denominator 9 end fraction close parentheses F minus fraction numerator 20 over denominator 3 end fraction. Hence graph between ℃ and ℉ will be a straight line with positive slope and negative intercept
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    The area of circle centred at (1, 2) and passing through (4, 6) is

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    Three rods of same dimensions are arranged as shown in figure. They have thermal conductivities K subscript 1 end subscript comma K subscript 2 end subscript and K subscript 3 end subscript. The points P and Q are maintained at different temperatures for the heat to flow at the same rate along P R Q and P Q then which of the following options is correct

    The given arrangement of rods can be redrawn as follows

    It is given that H subscript 1 end subscript equals H subscript 2 end subscript
    rightwards double arrow fraction numerator K A left parenthesis theta subscript 1 end subscript minus theta subscript 2 end subscript right parenthesis over denominator 2 l end fraction equals fraction numerator K subscript 3 end subscript A left parenthesis theta subscript 1 end subscript minus theta subscript 2 end subscript right parenthesis over denominator l end fraction rightwards double arrow K subscript 3 end subscript equals fraction numerator K over denominator 2 end fraction equals fraction numerator K subscript 1 end subscript K subscript 2 end subscript over denominator K subscript 1 end subscript plus K subscript 2 end subscript end fraction

    Three rods of same dimensions are arranged as shown in figure. They have thermal conductivities K subscript 1 end subscript comma K subscript 2 end subscript and K subscript 3 end subscript. The points P and Q are maintained at different temperatures for the heat to flow at the same rate along P R Q and P Q then which of the following options is correct

    physics-General
    The given arrangement of rods can be redrawn as follows

    It is given that H subscript 1 end subscript equals H subscript 2 end subscript
    rightwards double arrow fraction numerator K A left parenthesis theta subscript 1 end subscript minus theta subscript 2 end subscript right parenthesis over denominator 2 l end fraction equals fraction numerator K subscript 3 end subscript A left parenthesis theta subscript 1 end subscript minus theta subscript 2 end subscript right parenthesis over denominator l end fraction rightwards double arrow K subscript 3 end subscript equals fraction numerator K over denominator 2 end fraction equals fraction numerator K subscript 1 end subscript K subscript 2 end subscript over denominator K subscript 1 end subscript plus K subscript 2 end subscript end fraction