{"id":47356,"date":"2024-02-17T08:05:08","date_gmt":"2024-02-17T02:35:08","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=47356"},"modified":"2024-02-17T16:15:47","modified_gmt":"2024-02-17T10:45:47","slug":"plus-one-physics-chapter-wise-questions-answers-chapter-7","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/plus-one-physics-chapter-wise-questions-answers-chapter-7\/","title":{"rendered":"Plus One Physics Chapter Wise Questions and Answers Chapter 7 Systems of Particles and Rotational Motion"},"content":{"rendered":"

Kerala Plus One Physics Chapter Wise Questions and Answers Chapter 7 Systems of Particles and Rotational Motion<\/h2>\n

Plus One Physics Systems of Particles and Rotational Motion One Mark Questions and Answers<\/h3>\n

Question 1.
\nThe dimension of angular momentum is
\n(a) M\u00b0L1<\/sup>T-1<\/sup>
\n(b) M1<\/sup>L2<\/sup>T2<\/sup>
\n(c) M1<\/sup>L2<\/sup>T-1<\/sup>
\n(d) M2<\/sup>L1<\/sup>T-2<\/sup>
\nAnswer:
\n(c) M1<\/sup>L2<\/sup>T-1<\/sup>
\nAngular momentum = Moment of inertia x angular velocity
\n(Angular momentum) = [M1<\/sup>L2<\/sup>][T-1<\/sup>] = [M1<\/sup>L2<\/sup>T-1<\/sup>].<\/p>\n

Question 2.
\nIf the density of material of a square plate and a circular plate shown in figure is same, the centre of mass of the composite system will be
\n\"Plus
\n(a) inside the square plate
\n(b) inside the circular plate
\n(c) at the point of contact
\n(d) outside the system
\nAnswer:
\n(a) inside the square plate<\/p>\n

Question 3.
\nWhy spokes are provided in by cycle wheel?
\nAnswer:
\nThis increases moment of inertia even when the mass is small. This ensures uniform speed.<\/p>\n

Question 4.
\nA ballet dancer, an acrobat and an ice skater make use of an important principle in physics. Which is that principle?
\nAnswer:
\nConservation of angular momentum.<\/p>\n

Question 5.
\nA cat is able to land on her feet after a fall. Which principle of physics is being used by her?
\nAnswer:
\nPrinciple of conservation of angular momentum.<\/p>\n

Question 6.
\nA body is rotating in steady rate. What is torque acting on the body?
\nAnswer:
\nZero. Torque is required only for producing angular acceleration.<\/p>\n

Question 7.
\nA flywheel is revolving with constant angular velocity. A chip of its rim breaks and flies away. What will be the effect on the angular velocity?
\nAnswer:
\nThe reduction in mass will decrease moments of inertia. Hence angular velocity will be increased in order to conserve angular momentum.<\/p>\n

Question 8.
\nIs radius of gyration of a body constant quantity?
\nAnswer:
\nNo. It changes with change in position of the axis of rotation.<\/p>\n

Question 9.
\nWhat is another name for angular momentum?
\nAnswer:
\nMoment of momentum.<\/p>\n

Plus One Physics Systems of Particles and Rotational Motion Two Mark Questions and Answers<\/h3>\n

Question 1.
\nMoments of inertia of some bodies with axis are given in the table below. Fill in the blanks
\n\"Plus
\nAnswer:
\n\"Plus<\/p>\n

Question 2.
\nMatch the following:<\/p>\n\n\n\n\n\n\n\n\n\n
(a) Moment of force<\/td>\n\u03a4 \u2206 \u03b8<\/td>\n<\/tr>\n
(b) F\u2206r<\/td>\nLinear motion<\/td>\n<\/tr>\n
(c) Couple<\/td>\nTorque<\/td>\n<\/tr>\n
(d) 1\/2 I\u03c92<\/sup><\/td>\n\u03a4 \u2206 r<\/td>\n<\/tr>\n
<\/td>\nRotational motion<\/td>\n<\/tr>\n
<\/td>\n1\/2 MR2<\/sup><\/td>\n<\/tr>\n
<\/td>\nL2<\/sup>\/2I<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Answer:
\n(a) Torque
\n(b) \u03c4 \u2206 \u03b8
\n(c) Rotational motion
\n(d) \\(\\frac{1}{2} \\frac{L^{2}}{1}\\).<\/p>\n

Question 3.
\nA cat is able to function its feet after a fall, taking the advantage of principle of conservation of angular momentum.<\/p>\n

    \n
  1. Give the law of conservation of a angular momentum.<\/li>\n
  2. Explain how cat is able to do so<\/li>\n<\/ol>\n

    Answer:
    \n1. When there is no external torque, the total angular momentum of a body or a system of bodies are a constant.
    \n\u03c4 = \\(\\frac{d L}{d t}\\) (when \u03c4 = 0 , we get \\(\\frac{d L}{d t}\\) = 0).
    \nie L = constant.
    \nBut L = I\u03c9
    \n\u2234 I\u03c9 = a constant.<\/p>\n

    2. When a cat falls, it stretches its body. So that the moment of inertia becomes large. As I\u03c9 = constant, the value of angular speed will be decreased due to the increased value of moment of inertia. So cat lands on its feet gently.<\/p>\n

    Question 4.
    \nIf the polar ice cap melts what will happen to the length of the day?
    \nAnswer:
    \nFor earth, angular momentum is a constant (L\u03c9 = constant, ie no torque acts on the earth). When the polar ice cap melts, the water thus formed will flow down to the equatorial region.<\/p>\n

    The accumulation of water in equatorial line will increase the moment of inertia I of earth. In order to keep the angular momentum as a constant, \u03c9 will decrease. The decrease in \u2018\u03c9\u2019will increase the length of day.<\/p>\n

    Question 5.
    \nA girl has to lean towards right when carrying a bag in her left hand. Why?
    \nAnswer:
    \nWhen a girl carries her bag in her left hand, the centre of gravity of system will shift towards left. In order to bring it in the middle, the girl has to lean towards right.<\/p>\n

    Question 6.
    \nIf the earth loses the atmosphere what will happen to the length of the day?
    \nAnswer:
    \nFor earth, the angular momentum (L = I\u03c9) is a constant, because there is no torque acting on it. When earth loses the atmosphere, I decreases and \u03c9 increases to keep L as constant. Hence length of the day decreases.<\/p>\n

    Question 7.
    \nA girl standing on a turn table. What happens to the rotation speed, if she stretches her hand?
    \nAnswer:
    \nlf a girl rotating with a uniform speed on turn table, it\u2019s angular momentum (L = I\u03c9) will be a constant. When she suddenly stretches her hand, I Increases and \u03c9 decreases to keep L as constant.<\/p>\n

    Question 8.
    \nHow does a circus acrobat and a diver take advantage of conservation of angular momentum? Answer:
    \nThe diver while leaving the spring board, is throwing himself in a rotating motion. When he brings his hands and legs close, I decrease and \u03c9 increases. But before reaching water he will stretch his hands and legs. Hence I increases and \u03c9 decreases. So, that he gets a smooth entry into the water.<\/p>\n

    Plus One Physics Systems of Particles and Rotational Motion Three Mark Questions and Answers<\/h3>\n

    Question 1.
    \nA rigid body consists of \u2018n\u2019 particles of mass m1, m2, m3,……The body rotates about an axis with
    \nan angular velocity \u03c91, \u03c92, \u03c93……..<\/p>\n

      \n
    1. Starting from the kinetic energy of a single particle, arrive at an equation for kinetic energy of rotation.<\/li>\n
    2. Moment of inertia is also called rotational inertia. Why?<\/li>\n<\/ol>\n

      Answer:
      \n1. Consider a body rotating about an axis passing through some point O with uniform angular velocity \u2018\u03c9\u2019. The body can be considered to be made up of a number of particles of masses m1, m2, m3……etc at distances r1, r2, r3……etc. All the particles will have same angular velocity \u03c9 But their linear velocities will be different say v1, v2, v3…….etc.
      \n\"Plus
      \nK.E of 1st<\/sup> particle = \\(\\frac{1}{2}\\)m1<\/sub>v1<\/sub>2<\/sup>
      \n\\(\\frac{1}{2}\\)m1<\/sub>(r1<\/sub>\u03c9)2<\/sup>
      \n(\u2235 v = r\u03c9)
      \nK.E of IInd<\/sup> particle = \\(\\frac{1}{2}\\)m2<\/sub>(r2<\/sub>\u03c9)2<\/sup>
      \n\u2234 K.E of whole body =
      \n\"Plus
      \nBut we know moment of inertia,
      \n\"Plus
      \n\u2234 KE = \\(\\frac{1}{2}\\)I\u03c92<\/sup>
      \n2. Rotation inertia is measured in terms of moment of inertia. Hence moment of inertia is also called rotational inertia.<\/p>\n

      Question 2.
      \nThe handle of a door is always found at one edge of the door which is located at a maximum possible distance away from hinges.<\/p>\n

        \n
      1. Give reason for it.<\/li>\n
      2. In which direction will the torque act while the door opens inside the room?<\/li>\n
      3. If the door handle is fixed at the middle of the door, what difference do you feel in the applied force to open the door.<\/li>\n<\/ol>\n

        Answer:
        \n1. Torque \u03c4 = r F sin \u03b8
        \nFrom the above equation it is clear that, we get maximum torque when the handle of a door is located at a maximum possible distance (r) away from hinge.<\/p>\n

        2. The direction of torque is always along the axis of rotation of door.<\/p>\n

        3. If the door handle is fixed at middle, more force must be applied to get maximum torque that is required to open the door.<\/p>\n

        Question 3.
        \nMoment of inertia depends on the mass, axis of rotation and distribution of mass of the body.<\/p>\n

          \n
        1. What are moment of inertia and radius of gyration?<\/li>\n
        2. How will you distinguish a hard boiled egg from a raw egg by spinning each on the table.<\/li>\n<\/ol>\n

          Answer:
          \n1. Moment of inertia I = mr2<\/sup>
          \nRadius of gyration K = \\(\\sqrt{\\frac{I}{m}}\\).<\/p>\n

          2. A raw egg has more monemt of inertia than boiled egg. Hence raw egg spins more time than boiled egg.<\/p>\n

          Question 4.
          \nTable below given analogy between translational and rotational motions. Match the following.
          \n\"Plus
          \nAnswer:
          \n\"Plus<\/p>\n

          Plus One Physics Systems of Particles and Rotational Motion Four Mark Questions and Answers<\/h3>\n

          Question 1.
          \n1. Show that the total angular momentum of a rotating system remains constant if no torque acts on the system
          \n\"Plus
          \n2. A disc of moment of inertia I1<\/sub> is rotating freely with angular speed \u03c91 and a second non rotating disc with moment of inertia I2<\/sub> is dropped on it as shown in the figure. The two then rotate as one unit. Find the angular speed of rotation of the system.
          \nAnswer:
          \n1. we know torque \u03c4 = \\( \\frac{d L}{d t}\\)
          \nif \u03c4 = 0, we get \\( \\frac{d L}{d t}\\) = 0
          \nie. L = constant.<\/p>\n

          2. we know if torque acting on the body is zero, its angular momentum will be conserved
          \nie. I1<\/sub>\u03c91<\/sub> = I2<\/sub>\u03c92<\/sub>
          \nangular momentum of system, \u03c92<\/sub> = \\(\\frac{I_{1} \\omega_{1}}{\\left(I_{1}+\\mathrm{I}_{2}\\right)}\\).<\/p>\n

          Question 2.
          \nA rigid body can rotate an axis with a constant angular velocity and angular momentum L.<\/p>\n

            \n
          1. What is its moment of inertia about the axis?<\/li>\n
          2. Obtain a mathematical expression for rotational kinetic energy.<\/li>\n
          3. If the orientation of the axis of rotation changes, what happens to its moment of inertia<\/li>\n<\/ol>\n

            Answer:
            \n1. L = I\u03c9
            \nie. I = L\/\u03c9<\/p>\n

            2. Consider a rigid body rotating about an axis passing through the point O. Let co be the uniform angular velocity of the body.
            \n\"Plus
            \nThe body is imagined to be made up of large number of particles. Consider one such particle of mass \u2018m\u2019 at a distance \u2018r\u2019 from the axis of rotation.
            \nLinear Velocity of the particle v = r\u03c9
            \nK.E of the particle = 1\/2mv2<\/sup> = 1\/2 mr2<\/sup>\u03c92<\/sup>
            \nK.E of whole body = \u03a31\/2mr2<\/sup>\u03c92<\/sup> = 1\/2\u03c92<\/sup>\u03a3mr2<\/sup>
            \nK.E = 1\/2I\u03c92<\/sup>
            \nWhere \u03a3mr2<\/sup> = I, moment of inertia of the body.<\/p>\n

            3. Moment of inertia will be changed.<\/p>\n

            Question 3.
            \nA platform diver holds his hands and legs straight and makes loops in air before entering into water.<\/p>\n

              \n
            1. State the principle behind this.<\/li>\n
            2. What happens when he tries to land in the pool by stretching his arms and legs?<\/li>\n
            3. In the above situation, rotational kinetic energy is not conserved. Explain.<\/li>\n<\/ol>\n

              Answer:
              \n1. Conservation of angular momentum
              \nStatement<\/span>
              \nConservation of angular momentum states that, if the total torque acting on a system is zero, its angular momentum will be conserved.<\/p>\n

              2. Angular velocity decreases.<\/p>\n

              3. Initial kinetic energy K.E1<\/sub> = \\(\\frac{L^{2}}{2 I_{1}}\\) ____(1)
              \nwhere I1<\/sub> is the moment of inertia of diver when he makes loops in air
              \nfinal kinetic energy K.E2<\/sub> = \\(\\frac{L^{2}}{2 I_{2}}\\) _____(2)
              \nwhere I2<\/sub> is the moment of inertia of diver when he stretches his hands
              \nBut I1<\/sub> < I2<\/sub>
              \nHence from eq(1) and eq(2), we get
              \nKE1<\/sub> > KE2<\/sub>
              \nwhich means that rotational kinetic is not conserved.<\/p>\n

              Question 4.
              \nMoment of inertia of a thin ring of radius R about an axis passing through any diameter is 1\/2MR2<\/sup><\/p>\n

                \n
              1. What is the radius of gyration of the ring about an axis passing through any diameter.<\/li>\n
              2. A thin metal ring of radius 0.25m and mass 2kg starts from rest and roll down an inclined plane. If the linear velocity on reaching the foot of the plane is 2m\/s, calculate its rotational kinetic energy at that instant.<\/li>\n<\/ol>\n

                Answer:
                \n1.
                \n\"Plus<\/p>\n

                2.
                \n\"Plus<\/p>\n

                Question 5.
                \n\"Plus
                \nFigures show the two different spinning poses of a ballet dancer.<\/p>\n

                  \n
                1. In which spinning pose, the ballet dancer has more angular speed?<\/li>\n
                2. State the principle used by the ballet dancer to increase his angular speed.<\/li>\n
                3. \u201cIn the above situation, rotational kinetic energy is not conserved\u201d – Justify this statement.<\/li>\n<\/ol>\n

                  Answer:
                  \n1. The pose shown in figure (B).<\/p>\n

                  2. Statement of conservation of angular momentum.<\/p>\n

                  3. I1<\/sub>\u03c91<\/sub> = I2<\/sub>\u03c92<\/sub>
                  \n1\/2 I1<\/sub>2<\/sup>\u03c91<\/sub>2<\/sup> = 1\/2 I2<\/sub>2<\/sup>\u03c92<\/sub>2<\/sup>
                  \nI1<\/sub>(1\/2 I1<\/sub>\u03c91<\/sub>2<\/sup>) = (1\/2 I2<\/sub>\u03c92<\/sub>2<\/sup>)I2<\/sub>, I1<\/sub> > I2<\/sub>
                  \n(1\/2 I2<\/sub>\u03c92<\/sub>2<\/sup>) > 1\/2I1<\/sub>\u03c91<\/sub>2<\/sup><\/p>\n

                  Plus One Physics Systems of Particles and Rotational Motion Five Mark Questions and Answers<\/h3>\n

                  Question 1.
                  \nThe moment of inertia of a thin ring of radius R about an axis passing through any diameter is \\(\\frac{1}{2}\\)MR2<\/sup><\/p>\n

                    \n
                  1. To find the moment of inertia of the same ring about an axis passing through its centre of mass and perpendicular to its plane, which of the following theorem is used and state the theorem.\n