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Physics Test - 15

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Physics Test - 15
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  • Question 1
    1 / -0

    A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes an uncompressed spring and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10,000 N/m. The spring compresses by

    Solution

    Let x be the compression of the spring. The kinetic energy of the block=12mv2is used

    (i) Importing potential energy=12kx2to the spring and

    (ii) Doing work=fxagainst friction. Thus,

    12mv2-12kx2+fx

    12×2×42-12×10,000×x2+15x

    5000x2+15x-16=0

    The two roots arc

    x=-15±152+4×5000×161/22×5000

    =-15±225+320,0001/210,000

    =-15±55610,000=0.0551mand-0.0581m

    Since negative value of x is not permissible, x = 0.0551 m = 5.51 cm.

  • Question 2
    1 / -0

    Directions: In the following question, Statement - 1 (Assertion) is followed by Statement - 2 (Reason). The question has four options, out of which only one is correct.

    Statement – 1: A coil is connected in series with a bulb and this combination is connected to an a.c. source. If an iron core is inserted in the coil, the brightness of the bulb will be reduced.

    Statement – 2: When an iron core is inserted in the coil, its inductance decreases.

    Solution

    The correct choice is (3). If an iron core is inserted in the coil, its inductance L increase. Hence its reactance wL increases causing a decrease in the current in the circuit. As a result, the brightness of the bulb will reduce.

  • Question 3
    1 / -0

    Using mass (M), length (L), time (T) and current (A) as fundamental quantities, the dimensions of permeability are

    Solution

    Magnetic field due to long solenoid is

    B=μonl

    μo=Bnl

    =MLT-2/ALL-1A

    =MLT-2A-2

  • Question 4
    1 / -0

    In a sample of radioactive material, what fraction of the initial number of active nuclei will remain undisintegrated after half of a half-life of the sample ?

    Solution

  • Question 5
    1 / -0

    A cylindrical vessel of radius r is filled with a liquid to a height h such that the force exerted by the liquid on the sides of the vessel is equal to that exerted at the bottom. The ratio h/r is

    Solution

    Pressure at the bottom = hpg. Therefore, the force exerted at the bottom isF1=hpg×πr2.
    Now, since the mass of the liquid can be regarded as being concentrated at its centre of mass which is at a height h/2, the pressure on the sides=h2pg.

    Therefore, force exerted on sides is,

    F2=h2pg×2πrh.GivenF1=F2,or

    hpg×πr2=h2pg×2πrh

    Which gives r = h.

  • Question 6
    1 / -0

    Constant forces P=2i^5ȷ^+6k^ and Q=i^+2ȷ^k^ act on a particle. The work done when the particle is displaced from A whose position vector is 4ı^3ȷ^2k^, to B whose position vector is 6ı^+ȷ^3k^, is:

    Solution

    Let's say that the forces acting on the particle are P=2ı^5ȷ^+6k^ and Q=ȷ^+2ȷ^k^.

    The resulting force acting on the particle will be F=P+Q.

    F=(2ı^5ȷ^+6k^)+(ı^+2ȷ^k^)

    F=ı^3ȷ^+5k^

    Since the particle is moved from the point 4ı^3ȷ^2k^ to the point 6ı^+ȷ^3k^, the displacement vector D will be:

    D=AB=BA

    =(6ı^+ȷ^3k^)(4ı^3ȷ^2k^)

    =2ı^+4ȷ^k^

    And finally, the work done W will be:

    W=FD

    =(ı^3ȷ^+5k^)(2ı^+4ȷ^k^)

    =(1)(2)+(3)(4)+(5)(1)

    =2125

    =15 units

  • Question 7
    1 / -0

    One face of a glass prism is silver polished. A light ray falls at an angle of 45° on the other face. After refraction, it is subsequently reflected from the silvered face and then, it retraces its path. The refracting angle of the prism is 30°. The refractive index of the material of the prism is

    Solution

    The refracted ray QR will retrace its path if it falls normally on the silvered face AB (see adjoining figure). It follows from Fig. that

  • Question 8
    1 / -0

    Two blocks of masses m1 = 3 m and m2 = 2 m are suspended from a rigid support by inextensible uniform wires A and B. Wire A has negligible mass and wire B has a mass m3 = m as shown in the figure. The whole system of blocks, wires and the support has an upward acceleration a.

    The tension at the mid-point C of wire B is

    Solution

    Refer to Fig. Let T be the tension at the mid-point C of wire B. Then,

  • Question 9
    1 / -0

    Which of the following is non-conservative force?

    Solution

    Electrostatic force, gravitational force and spring force are the conservative forces because the workdone by these forces is path independent whereas viscous force is a non-conservative force as the work done by this force is path dependent.

  • Question 10
    1 / -0

    A small trolley of mass 2 kg resting on a horizontal frictionless turntable is connected by a light spring to the centre of the table. The relaxed length of the spring is 35 cm. When the turntable is rotated at an angular frequency of 10 rad s–1, the length of the spring becomes 40 cm. What is the force constant of the spring?

    Solution

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