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Weekly Quiz Competition
  • Question 1
    1 / -0
    A small solid sphere of radius R made of a material of bulk modulus B is surrounded by an incompressible liquid in a cylindrical container. A massless piston of area A floats on the surfaces of the liquid. Find the magnitude of frictional change in the radius of the sphere (dR/R) when a mass M is placed slowly on the piston to compress the liquid.

    Solution
    V =





  • Question 2
    1 / -0
    Find the value of r so that maximum power is generated in external circuit.

    Solution
    Equivalent resistance across network
    For maximum power generation,

  • Question 3
    1 / -0
    The air of density ρ and moving with a velocity v strikes perpendicularly the inclined surface of area A and of a wedge kept on a horizontal surface. The mass of the wedge is m. Assuming the collisions to be perfectly inelastic, the minimum value of the coefficient of friction between the wedge and the ground so that the wedge does not move is: (Assume that mass of particles of air is negligible)

    Solution
    vertical force balance

    N = mg + ρAv2 cos ............(1)

    Horizontal force balance

    ρAv2 sin ....................(2)

    From eq.(1) and (2)

  • Question 4
    1 / -0
    In a YDSE apparatus, the source (wavelength λ) is kept as shown in the figure. None of the slits receives direct light but gets it after reflection by mirrors as shown in the figure. If d = 100λ and D = 50000λ, then the distance of central maxima from the centre of the screen is:

    Solution
    Due to reflection, phase difference of p is included in upper wave.
    Hence, central maxima position

  • Question 5
    1 / -0
    A straight small object is kept in front of a convex lens, as shown in the figure. Which among the following shows the right image of the object?

    Solution

  • Question 6
    1 / -0
    Two identical balls of radii r are kept on a horizontal plane with their centres d distance apart. A third ball, identical to previous ones, collides elastically with both the balls symmetrically as shown in the figure. If the third ball comes to rest after the collision, d should be

    Solution

  • Question 7
    1 / -0
    One mole of an ideal gas is carried through a thermodynamic cycle as shown in the figure. The cyclic process consists of an isochoric, an isothermal and an adiabatic process. Find the adiabatic exponent of gas.

    Solution
    CA is adiabatic and. BC is isothermal as per slope.

    Hence
    Using PVr = constant

  • Question 8
    1 / -0
    The figure below shows roughly how the force (F) between two adjacent atoms in a solid varies with separation (r).

    (i) OQ is equilibrium separation.
    (ii) Hooke`s law is obeyed around P
    (iii) The potential energy of the atom is the gradient of the graph at all points.
    (iv) The energy to separate the atoms completely is obtained from the area enclosed below the axis of r.

    Solution
    (i) Q is not equilibrium because U is not minimum there.
    (ii) correct
    (iii) Wrong because
    (iv) = dissociation energy Þ correct
  • Question 9
    1 / -0
    In the situation as shown in figure, if acceleration of B is 'a', then find the acceleration of A.

    Solution




    In DABC,



    Þ aA = 2a cos
  • Question 10
    1 / -0
    A semicircular disc of mass 'M' and radius 'R' is let from rest from a vertical position as shown. Assuming that the disc does not slip, the initial magnitude of angular acceleration of the disc will be:

    Solution
    C.O.M. of semicircular disc is at distance of 4R/3π from centre.

    Torque = (Mg)(4R/3π)
    Moment of inertia, I, about the axis normal to semicircular disc through pt. of intersection with ground =
    now
    = 8g/9πR
  • Question 11
    1 / -0
    A solid cone of height H and radius R suspended by a string is just submerged in a liquid of density p as shown in the figure. The magnitude of the net force applied by the liquid on the curved surface of the cone is: (Po is the atmospheric pressure)

    Solution
    There will be only vertically downward force on the curved surface of the cone (applied by the liquid) as the horizontal force will be cancelled.
    Let this force be F.
    Buoyancy force


  • Question 12
    1 / -0
    In a sample of hydrogen like atoms all of which are in ground state, a photon beam containing photons of various energies is passed. In absorption spectrum, five dark lines are observed. The number of bright lines in the emission spectrum will be: (Assume that all transitions take place)
    Solution
    Since five dark lines are observed in the absorption spectrum, the highest excited state of the atom is n = 6.
    Therefore, number of bright lines possible in the emission spectrum =
  • Question 13
    1 / -0
    In a sample of rock, the ratio of 206Pb to 238U nuclei is found to be 0.5. The age of the rock is: (Assume that all the Pb nuclides in the rock was produced due to the decay of Urarium nuclides and
    Solution
    Let No be the initial number of active nuclides of 238U.

    Given

    From above
  • Question 14
    1 / -0
    A thin plane convex glass lens ( = 1.5) has its plane surface silvered and R is the radius of curvature of the curved part. Then, which of the following ray diagrams is the correct representation for an object placed at O?
    Solution


    After reflection from the spherical surface, the ray becomes parallel to optic axis. Hence, after reflection from silvered surface, it will retrace its initial path and image coincides with object.
  • Question 15
    1 / -0
    Initially, a spring is compressed by distance x0 from equilibrium position. At this compression, the block is given velocity, so that compression in the spring increases and the block starts executing S.H.M. (Spring constant is K). Equation of motion of the block is:

    Solution

    ;

    => = ;

    =>

    Equation satisfies the condition given in the question.
  • Question 16
    1 / -0
    A sample of radioactive material has mass m, decay constant , molecular weight M and Avogadro constant NA. The initial activity of the sample is
    Solution
    Activity = number of disintegrations per unit time = where N = total number of nuclei

    Also, N = number of


  • Question 17
    1 / -0
    The instantaneous height and position of a projectile are given by x = 6t, y = 8t - 5t2 metre. What is the initial speed of the projectile? (`t` is in seconds)
    Solution
    x = 6t



    Y = 8t - 5t2



    At

    Initial velocity =
  • Question 18
    1 / -0
    The fundamental frequency of a sonometer wire of length `` is fo. A bridge is now introduced at a distance of from the centre of the wire . The number of beats heard, if both sides of the bridges are set into vibration in their fundamental modes, is
    Solution


    Beat frequency = f1 - f2 =

  • Question 19
    1 / -0
    A capillary tube of radius `r` is immersed in water and water rises in it to a height `h`. The mass of water in the capillary tube is `m`. Another capillary of radius 2r is immersed in water. The mass of water that will rise in this tube is:
    Solution
    Mass =

    Here, h =

    From above



    `r` is doubled, so mass of water in capillary will also become two times.
  • Question 20
    1 / -0
    A plano-concave lens fits into a plano-convex lens and their plane surfaces are parallel to each other. If lenses are made of different materials having refractive indices and and the radius of curvature of the curved surfaces is R, find the focal length of the system.

    Solution




  • Question 21
    1 / -0
    There is a man of mass 100 kg sitting on a motorbike of mass 150 kg. The distance between axles of the wheels (wheelbase) is 1.5 m. The common centre of mass of the man and motorbike is at a height of I m above ground and at a distance of 0.6 m from the vertical line going through the rear axle. Then, (Take g = 10 m/s2)
    Solution
    N2 = 0, f2 = 0
    f1 = ma
    N1 = 2500 N 0.6 = f1 1

    As net torque about C = zero
    2500 0.6 = 250 a 1
    a = 6m/s2
     Also ma =


  • Question 22
    1 / -0
    A point object is projected from a point on the principal axis of a concave mirror of focal length 20 cm with a speed of m/s at an angle of tan-1 2 with the principal axis as shown in figure. Choose the correct option. (Consider the moment just after projection)

    Solution


    v = ?

    f = -20 cm







    vsx =





  • Question 23
    1 / -0
    The molar heat capacity C of an ideal gas in a process is given by C = a/T, where `a` is a constant. If the work done by one mole of gas during heating from To to nTo through the same process will be
    Solution




  • Question 24
    1 / -0
    A satellite is projected with velocity times its escape speed from Earth`s surface. The initial velocity of the satellite is parallel to the surface of Earth. The maximum distance of the satellite from the centre of Earth will be
    Solution
    According to the principle of conservation of angular momentum,



    Applying principle of conservation of mechanical energy,



    Solving the above equations, we get h = 4R.
  • Question 25
    1 / -0
    A particle is projected from point A at an angle of 53o with horizontal. At the same time, the wedge starts from rest and moves with constant acceleration 'a' as shown. The value of 'a' for which the particle strikes the plane perpendicular to it at P is:

    Solution
    Let the height of point P above the ground be h.

    u(cos53o) (t) + h = ...(1)

    ...(2)

    h = ut sin53o - ...(3)
    From equations (1) and (3), comparing the values of h, we get

     ...(4)

    Putting the value of 't' in equation (4) from equation (2), we get



    Hence, we get a = 13g = 130 m/s2
  • Question 26
    1 / -0
    A transverse wave is travelling along negative y-axis whose snap shot is given at any instant of time t. Find out the points which are having velocity in negative x-direction.

    Solution
    Particle velocity, vp = -slope
    If vp is positive, then it is along positive x-axis; and if it is negative, it is along negative x-axis.
  • Question 27
    1 / -0
    Energy required to remove one electron from neutral helium atom is E1 eV. Energy required to remove both electrons form a neutral helium atom is
    Solution
    After removing one electron, helium atom will behave like hydrogen atom.

    So, total energy



  • Question 28
    1 / -0
    A small air bubble is inside a transparent-sphere made of two different material having refractive indices and . The radius of sphere is 10 cm. If the position of bubble is 8 cm from the bottom, then what will be the approximate apparent depth of the bubble when viewed normal?

    Solution
    For curved surface,



    Now



  • Question 29
    1 / -0
    A particle is projected with a velocity of 10 ms-1 at an angle 37o with horizontal. A bird moves along the path of projected particle with constant speed of 4 ms-1. Find the acceleration of bird when it is at the highest point of path of particle. (Take g = 10 ms-2)
    Solution
    For particle, Mg =



    For bird, an =

    = = 2.5 ms-2
  • Question 30
    1 / -0
    The mass of the astronauts in a space station cannot be checked with the scales used on the Earth. Instead we use a spring balance, which oscillates when a mass is suspended from it. Imagine a seat of a mass of 20 kg, which oscillates with a frequency of 2 Hz. After the astronaut sits in the seat, the frequency decreases to 1 Hz. How much is the mass of the astronaut?
    Solution
    T = 2











    k = 4(20)

    Now





    20 + m = 80

    m = 60 kg
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