Std XII Physics Test - Rotational Dynamics PDF

Std XII: PHYSICS TEST – ROTATIONAL DYNAMICS (Time Du ratio n : 1.5 h o u rs , Marks : 35) Q 1. Choose the right answer from the alternatives given: [4M] i. A thin-walled hollow cylinder is rolling down an incline, without slipping. At any in...

Std XII: PHYSICS TEST – ROTATIONAL DYNAMICS (Time Du ratio n : 1.5 h o u rs , Marks : 35) Q 1. Choose the right answer from the alternatives given: [4M] i. A thin-walled hollow cylinder is rolling down an incline, without slipping. At any instant, the ratio “Rotational K.E.: Transational K.E.: Total K.E.” is: a) 1:1:2 c) 1:1:1 b) 1:2:3 d) 2:1:3 ii. In a certain unit, the radius of gyration of a uniform disc about its central and transverse axis is √2.5. its radius of gyration about a tangent in its plane (in the same unite) must be: a) √5 d) √12.5 b) 2.5 c) 2√2.5 iii. When seen from below, the blades of a ceiling fan are seen to be revolving anticlockwise and their speed is decreasing. Select correct statement about the directions of its angular velocity and angular acceleration. a) Angular velocity upwards, acceleration downwards b) Angular velocity downwards, angular acceleration upwards c) Both, angular velocity and angular acceleration, upwards d) Both, angular velocity and angular acceleration, downward iv. Select correct statement about the expression of moment of inertia (M.I.) in terms of mass M of the object and some of its distance parameter/s, such as R, L, etc. a) Different objects must have different expressions for their M.I. b) When rotating about their central axis, a hollow right circular cone and a disc have the same expression for the M.I. c) Expression for the M.I. for a parallelepiped rotating about the transverse axis passing through its centre includes its depth. d) Expression for M.I. of a rod and that of a plane sheet is the same about a transverse axis. Q 2. Answer the following [6M] i. Derive an expression for a maximum safety speed with which a vehicle should move along a curved horizontal road. ii. Do we need a banked road for a two-wheeler? Explain iii. A uniform disc and a hollow right circular cone have the same formula for their M.I., when rotating about their central axes. Why is it so? Q 3. Answer the following: (3 Marks each) [15M] i. Derive an expression that relates angular momentum with the angular velocity of a rigid body. ii. A ceiling fan having moment of inertia 2 kg-m2 attains its maximum frequency of 60 rpm i n ‘ 2𝜋’ seconds. Calculate its power rating. iii. A metallic ring of mass 1 kg has moment of inertia 1kg m 2 when rotating about one of its diameters. It is molten and remoulded into a thin uniform disc of the same radius. How much will its moment of inertia be, when rotated about its own axis. iv. State and explain the principle of conservation of angular momentum. v. Discuss the interlink between translational, rotational and total kinetic energies of a rigid object that rolls without slipping. “There is nothing heavier in scales than good character” – Prophet Muhammad. Std XII: PHYSICS TEST – ROTATIONAL DYNAMICS (Time Du ratio n : 1.5 h o u rs , Marks : 35) Q 4. Answer the following: i. A rigid object is rolling down an inclined plane. Derive expressions for the acceleration along the track and the speed after falling through a certain vertical distance. [4M] ii. Part of a racing track is to be designed for a curvature of 72 m. we are not recommending the vehicles to drive faster than 216 kmph. With what angle should the road be tilted? By what height will its outer edge be, with respect to the inner edge if the track is 10 m wide? [3M] iii. Starting from rest, an object rolls down along an incline that rises by 3 in every 5 (along it). The 5 object gains a speed of √ 10 𝑚/𝑠 as it travels a distance of 𝑚 along the incline. What can be the 3 possible shape of the object? [3M] “There is nothing heavier in scales than good character” – Prophet Muhammad.