| Previous Year Questions of March Examinations from 2010 to 2020 |
| Chapter Name: SYSTEM OF PARTICLES AND ROTATIONAL MOTION |
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Ramesh observes the motion of an insect in a circle. He finds that it travels 6 revolutions in an anticlockwise direction for a time of 31.4sec. a) Find the angular velocity of the insect. b) If the insect travels 4 revolutions in the clockwise direction for a time of 8.6sec, what will be the angular speed averaged over the total time? c) Obtain the expression for centripetal acceleration (a c ) in terms of angular speed (ω). |
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In a hammer throw event, a solid sphere of mass 16 kg is tied to a light 50 cm long chain. A sportsman gives to it a constant moment of 30 N-m for 10 seconds and then throws the sphere. Consider the sphere as a point mass. a) Find the moment of inertia about the axis of rotation. b) If ‘L’ is the angular momentum and ‘T ’ is the torque, show that T = dL/dt c) Write an example for the motion in which an angular momentum remains constant. OR Remya stands at the centre of a turn-table with her two arms outstretched. The table with an angular speed of 40 revolutions / minute. a) What will happen to the moment of inertia if she folds her hands back? b) If the angular speed is increased to 100 revolutions / minute, what will be the new moment of inertia? c) Write the expression for the rotational kinetic energy of the system and explain the terms involved in it. |
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a) The earth revolves around the sun in an elliptical orbit. The closet approach of the earth with the sun is called perihelion. When the approaches the perihelion, its speed increases. Explain this principle. b) A body rolls over horizontal, smooth surface without slipping with translational KE E. Show that the total KE of the body is E(1 + k2/R2). Where k is the radious of gyration and R is the radius of the body. c) a wheel of mass 1000 kg and radius 1 m is rotating at the rate of 420 rpm. What is the constant torque required to stop the wheel in 14 rotations. Assuming the mass to be concentrated at the rim of the wheel. |
| Rotational inertia is the tendency of a rotating body to resist any change in its state of rotational motion. a) What you mean by the radius of gyration of a rolling body? b) Show that the disc has the moment of inertia I = MR2/2 about an axis perpendicular to the disc at its centre. c) The figure shows two different spinning poses of a ballet dancer.In which spinning pose does the ballet dancer have less angular velocity? Justify your answer. |
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Moment of inertia is the analogue of mass in rotational motion. But unlike mass; it is not a fixed quantity. a) Moment of inertia can be regarded as a measure of rotational inertia. Why? b) Write any two factors on which the moment of inertia of a rigid body depends. c) The moments of inertia of two rotating bodies A and B are IA and IB (IA > IB ) and their angular momentum are equal. Which one has a greater kinetic energy? Explain. |
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Moment of inertia is the rotational analogue of mass in linear dynamics. Write the equation of the moment of inertia of a disc about an axis passing through its centre and perpendicular to its plane. a) State the parallel axis theorem of moment of inertia. b) A coin is rolling on a plane surface. What fraction of its total kinetic energy is rotational? |
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The rotational analogue of force is moment of force, also called torque. a) The turning effect of force is maximum when the angle between r and F is............. b) A wheel starting from rest acquires an angular velocity of 10 rad/s in two seconds. The moment of inertia of the wheel is 0.4 kg m2 . Calculate the torque acting on it. c) The possibility of falling backward with the ladder is more when you are high up on the ladder than when you just begin to climb. Explain why? |
| The demonstration of conservation of angular momentum is schematically shown in the figures. Identify the figure which has more angular velocity |
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The angular momentum of a partiole is the rotational analogue of its inear momentum. a) The equation connecting angular momentum and linear momentum is ....... i) L = r x p ii) L = p x r iii) L = r . p iv) L =(1/2) r x p b) Starting from the equation connecting angular momentum and linear momentum, deduce the relation between torque and angular momentum |
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Moment of inertia in rotational motion is analogus to mass in linear motion. a) The moment of inertia of a circular disc about an axis perpendicular to the plane, at the centre is given by ............... i) 1/4 MR2 ii) 1/6 MR2 iii) 3/2 MR2 iv) 1/2 MR2 b)State perpendicular axis theorem and by using the theorem, deduce the moment of inertia of the circular disc about an axis passing through the diameter |
| State the theorem of parallel axes on moment of inertia |
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A stone tied to the end of a string 80 cm long is whirled in a horizontal circle with a constant speed a) What is the angle between velocity and acceleration at any instant of motion? b) If the stone makes 14 revolutions in 25 s, what is the magnitude of acceleration of the stone? |
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a) Write e equation connecting torque with force b) A metre stick is balanced at its centre (50 cm). When two coins, each of mass 5 g, are put one on the top of the other at the 12 cm mark, it is found to be balanced at 45 cm. What is the mass of the stick? c) Derive the relation connecting torque with angular momentum |
Match the following
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Starting from the rest a solid sphere rolls down in an inclined plane of vertical height h, without slipping (a) If M is the mass and R is the radius of the sphere, write an equation for the moment of inertia of the above sphere about the diameter (b) Prove that the velocity with which the sphere reaches bottom of the plane if 1.2 √(gh) (c) If instead of sphere another object, of the same mass and radius with a different shape is used in the above experiment, will it reach the bottom with the same or different velocity? |
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The rotational analogue of force is (a) Energy (b) Work (c) Inertia (d) torque |
| A cord of negligible mass is wound round the rim of a flywheel mounted on a
horizontal axle as shown in figure : Calculate the angular acceleration of the wheel if steady pull of 25 N is applied on the cord. Moment of inertia of flywheel about its axis is ½ MR2 |
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| State theorem of perpendicular axes on moment of inertia. Derive an expression to find the moment of inertia of a circular disc about one of its diameters with the help of a neat diagram |
| What is the analogue of mass in rotational motion ? |
| Define angular velocity. Write the equation showing its relation with linear velocity |
| What are the factors on which the moment of inertia of a rigid body depends ? |
| A stone tied to the end of a string 80 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 25 s, what is the magnitude and direction of centripetal acceleration of the stone ? |
