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System of Particles and Rotational Motion Test - 4

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System of Particles and Rotational Motion Test - 4
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  • Question 1
    4 / -1

     

    A particle of mass m moves uniformly with a speed v along a circle of radius r. A and B are two points on the circle, such that the arc AB subtends an angle θ at the center of the circle. The magnitude of change in momentum as the particle moves from A to B is given by:

     

    Solution

     

     

    Assume particle is at lowest point of the circle

     

     

  • Question 2
    4 / -1

    An object comprises of a uniform ring of radius R and its uniform chord AB (not necessarily made of the same material) as shown. Which of the following can not be the centre of mass of the object.

                                    

    Solution




    Since the points must have symmetric coordinates so B is the answer.

  • Question 3
    4 / -1

     

    The kinetic energy of a moving body is given by K = 2v2, K being in joules and v in m/s. Its momentum when traveling with a velocity of 2 ms−1 will be :

     

    Solution

     

     

     

  • Question 4
    4 / -1

    Consider following statements

    [1] CM of a uniform semicircular disc of radius R = 2R/p from the centre

    [2] CM of a uniform semicircular ring of radius R = 4R/3p from the centre

    [3] CM of a solid hemisphere of radius R = 4R/3p from the centre

    [4] CM of a hemisphere shell of radius R = R/2 from the centre

    Which statements are correct?

  • Question 5
    4 / -1

     

    A wheel of moment of inertia 5 × 10−3 kgm2 is making 20 rev/s. The torque required to stop it in 10 s is :

     

    Solution

     


     

     

  • Question 6
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    The position of axis of rotation of a body is changed so that its moment of inertia decreases by 36%. Find the % change in its radius of gyration.

     

    Solution

     


     

  • Question 7
    4 / -1

     

    The radius of gyration of a rotating metallic disc is independent of which of the following physical quantity.

  • Question 8
    4 / -1

     

    A flywheel making 120 r.p.m is acted upon by a retarding torque producing angular retardation of π rad/s2. Time taken by it to come to rest is:

    Solution

     

     

  • Question 9
    4 / -1

     

    A body of mass 'M' collides against a wall with a velocity 'v' and retraces its path with the same velocity, the change in momentum is

    Solution

     

     

  • Question 10
    4 / -1

    The diagram to the right shown the velocity-time graph for two masses R and S that collided elastically. Which of the following statements is true?

                         

    (I) R and S moved in the same direction after the collision.

    (II) Kinetic energy of the system (R & S) is minimum at t = 2 milli sec.

    (III) The mass of R was greater than mass of S.

    Solution

    1. The velocities of both the masses are always positive hence same direction
    2. The KE will be min when Vr = Vs which is at 2ms
    3. The dpr/dt = dps/dt and as we can see in the graph dvr/dt < dvs/dt, so mass of R is greater

  • Question 11
    4 / -1

     

    A brass disc is rotating about its axis. If temperature of the disc is increased then its:

    Solution

     

     

  • Question 12
    4 / -1

     

    In a one-dimensional collision between two particles, their relative velocity is before the collision and  after the collision

     

  • Question 13
    4 / -1

     

    Four particles each of mass m are placed at the corners of a square of side length l. The radius of gyration of the system about an axis perpendicular to the square and passing through its center is:

    Solution

     

     

  • Question 14
    4 / -1

     

    The radius of gyration of rod of length L and mass M about an axis perpendicular to its length and passing through a point at a distance 3/L from one of its ends is:

     

    Solution

     

     

  • Question 15
    4 / -1

     

    I is moment of inertia of a thin rod of uniform thickness about an axis perpendicular to its length and passing through its centre. The rod at one of two sides of axis is cut and removed. The moment of inertia of remaining rod about same axis is :

    Solution

     

     

     

     

  • Question 16
    4 / -1

    A particle of mass m moving horizontal with v0 strikes a smooth wedge of mass M, as shown in figure. After collision, the ball starts moving up the inclined face of the wedge and rises to a height h.

    The final velocity of the wedge v2 is

  • Question 17
    4 / -1

     

    When the particle has risen to a height h on the wedge, then choose the correct alternative(s)

     

  • Question 18
    4 / -1

    The maximum height h attained by the particle is

  • Question 19
    4 / -1

    Identify the correct statement(s) related to the situation when the particle starts moving downward.

  • Question 20
    4 / -1

     

    Suppose the particle when reaches the horizontal surfaces, its velocity with respect to ground is v1 and that of wedge is v2. Choose the correct statement (s)

                          

     

  • Question 21
    4 / -1

    Choose the correct statement(s) related to particle m

  • Question 22
    4 / -1

     

    A body of mass m = 3.513 kg is moving along the x-axis with a speed of 5.00 ms−1. The magnitude of its momentum is recorded as :

    Solution

     

    Momentum of the body is mv = 3.513kg × 5.00m/s = 17.565kgm/s

    However, the accuracy of the result would be determined by the most inaccurate observation, which is speed with three significant digits. Thus the answer would be expressed in three significant digits, that is, 17.6 kgm/s

     

  • Question 23
    4 / -1

    A small ball B of mass m is suspended with light inelastic string of length L from a block A of same mass m which can move on smooth horizontal surface as shown in the figure. The ball is displaced by angle q from equilibrium position & then released.

                                    

    The displacement of block when ball reaches the equilibrium position is

  • Question 24
    4 / -1

    Tension in string when it is vertical, is

    Solution

    Tension in string when it is vertical, is Mg. Since nothing else has been provided so we assume all the forces are in the desired directions.

  • Question 25
    4 / -1

    Maximum velocity of block during subsequent motion of the system after release of ball is

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