# Balbharati solutions for Physics 12th Standard HSC Maharashtra State Board chapter 1 - Rotational Dynamics [Latest edition]

## Chapter 1: Rotational Dynamics

Exercises
Exercises [Pages 23 - 25]

### Balbharati solutions for Physics 12th Standard HSC Maharashtra State Board Chapter 1 Rotational Dynamics Exercises [Pages 23 - 25]

Exercises | Q 1.1 | Page 23

Choose the correct option.

When seen from below, the blades of a ceiling fan are seen to be revolving anticlockwise and their speed is decreasing. Select the correct statement about the directions of its angular velocity and angular acceleration.

• Angular velocity upwards, angular acceleration downwards.

• Angular velocity downwards, angular acceleration upwards.

• Both, angular velocity and angular acceleration, upwards.

• Both, angular velocity and angular acceleration, downwards.

Exercises | Q 1.2 | Page 23

Choose the correct option.

A particle of mass 1 kg, tied to a 1.2 m long string is whirled to perform the vertical circular motion, under gravity. The minimum speed of a particle is 5 m/s. Consider the following statements.

P) Maximum speed must be 55 m/s.
Q) Difference between maximum and minimum tensions along the string is 60 N.
Select the correct option.

• Only the statement P is correct.

• Only the statement Q is correct.

• Both the statements are correct.

• Both the statements are incorrect.

Exercises | Q 1.3 | Page 23

Choose the correct option.

Select correct statement about the formula (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.

• Different objects must have different expressions for their M.I.

• When rotating about their central axis, a hollow right circular cone and a disc have the same expression for the M.I.

• Expression for the M.I. for a parallelepiped rotating about the transverse axis passing through its centre includes its depth.

• Expression for M.I. of a rod and that of a plane sheet is the same about a transverse axis.

Exercises | Q 1.4 | Page 23

Choose the correct option.

In a certain unit, the radius of gyration of a uniform disc about its central and transverse axis is sqrt2.5. Its radius of gyration about a tangent in its plane (in the same unit) must be

• sqrt5

• 2.5

• 2sqrt2.5

• sqrt12.5

Exercises | Q 1.5 | Page 23

Choose the correct option.

Consider the following cases:

(P) A planet revolving in an elliptical orbit.
(Q) A planet revolving in a circular orbit.

Principle of conservation of angular momentum comes in force in which of these?

• Only for (P)

• Only for (Q)

• For both, (P) and (Q)

• Neither for (P), nor for (Q)

Exercises | Q 1.6 | Page 24

Choose the correct option.

A thin walled hollow cylinder is rolling down an incline, without slipping. At any instant, without slipping. At any instant, the ratio "Rotational K.E.: Translational K.E.: Total K.E." is

• 1: 1: 2

• 1: 2: 3

• 1: 1: 1

• 2: 1: 3

Exercises | Q 2.1 | Page 24

Exercises | Q 2.2 | Page 24

Do we need a banked road for a two-wheeler? Explain.

Exercises | Q 2.3 | Page 24

On what factors does the frequency of a conical pendulum depend? Is it independent of some factors?

Exercises | Q 2.4 | Page 24

Why is it useful to define the radius of gyration?

Exercises | Q 2.5 | Page 24

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?

Exercises | Q 3 | Page 24

While driving along an unbanked circular road, a two-wheeler rider has to lean with the vertical. Why is it so? With what angle the rider has to lean? Derive the relevant expression. Why such a leaning is not necessary for a four wheeler?

Exercises | Q 4.1 | Page 24

Using energy conservation, derive the expressions for the minimum speeds at different locations along a vertical circular motion controlled by gravity.

Exercises | Q 4.2 | Page 24

Using energy conservation, along a vertical circular motion controlled by gravity. Is a zero speed possible at the uppermost point? Under what condition/s?

Exercises | Q 4.3 | Page 24

Using energy conservation, along a vertical circular motion controlled by gravity, prove that the difference between the extreme tensions (or normal forces) depends only upon the weight of the objects.

Exercises | Q 5 | Page 24

Discuss the necessity of radius of gyration. Define it. On what factors does it depend and it does not depend? Can you locate come similarity between the center of mass and radius of gyration?​ What can you infer if a uniform ring and a uniform disc have the same radius of gyration?

Exercises | Q 6 | Page 24

State the conditions under which the theorems of parallel axes and perpendicular axes are applicable. State the respective mathematical expressions.

Exercises | Q 7 | Page 24

Derive an expression which relates angular momentum with the angular velocity of a rigid body​.

Exercises | Q 8 | Page 24

Obtain an expression for torque acting on a rotating body with constant angular acceleration. Hence state the dimensions and SI unit of torque.

Exercises | Q 9 | Page 24

State and explain the principle of conservation of angular momentum. Use a suitable illustration. Do we use it in our daily life? When?

Exercises | Q 10 | Page 24

Discuss the interlink between translational, rotation and total kinetic energies of a rigid object rolls without slipping.

Exercises | Q 11 | Page 24

A rigid object is rolling down an inclined plane derive the expression for the acceleration along the track and the speed after falling through a certain vertical distance.

Exercises | Q 12 | Page 24

Somehow, an ant is stuck to the rim of a bicycle wheel of diameter 1 m. While the bicycle is on a central stand, the wheel is set into rotation and it attains the frequency of 2 rev/s in 10 seconds, with uniform angular acceleration. Calculate:
(i) The number of revolutions completed by the ant in these 10 seconds.
(ii) Time is taken by it for first complete revolution and the last complete revolution.

Exercises | Q 13 | Page 24

The coefficient of static friction between a coin and a gramophone disc is 0.5. Radius of the disc is 8 cm. Initially the center of the coin is π cm away from the center of the disc. At what minimum frequency will it start slipping from there? By what factor will the answer change if the coin is almost at the rim?
(use g = π2m/s2)

Exercises | Q 14 | Page 25

Part of a racing track is to be designed for curvature of 72m. 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?

Exercises | Q 15 | Page 25

The road in question 14 above is constructed as per the requirements. The coefficient of static friction between the tyres of a vehicle on this road is 0.8, will there be any lower speed limit? By how much can the upper-speed limit exceed in this case?

Exercises | Q 16 | Page 25

During a stunt, a cyclist (considered to be a particle) is undertaking horizontal circles inside a cylindrical well of radius 6.05 m. If the necessary friction coefficient is 0.5, how much minimum speed should the stunt artist maintain? The mass of the artist is 50 kg. If she/he increases the speed by 20%, how much will the force of friction be?

Exercises | Q 17 | Page 25

A pendulum consisting of a massless string of length 20 cm and a tiny bob of mass 100 g is set up as a conical pendulum. Its bob now performs 75 rpm. Calculate kinetic energy and increase in the gravitational potential energy of the bob. (Use π2 = 10)

Exercises | Q 18 | Page 25

A motorcyclist (as a particle) is undergoing vertical circles inside a sphere of death. The speed of the motorcycle varies between 6 m/s and 10 m/s. Calculate the diameter of the sphere of death. How much minimum values are possible for these two speeds?

Exercises | Q 19 | Page 25

A metallic ring of mass 1 kg has a moment of inertia 1 kg m2 when rotating about one of its diameters. It is molten and remolded into a thin uniform disc of the same radius. How much will its moment of inertia be, when rotated about its own axis.

Exercises | Q 20 | Page 25

A big dumb-bell is prepared by using a uniform rod of mass 60 g and length 20 cm. Two identical solid spheres of mass 50 g and radius 10 cm each are at the two ends of the rod. Calculate the moment of inertia of the dumb-bell when rotated about an axis passing through its centre and perpendicular to the length.

Exercises | Q 21 | Page 25

A flywheel used to prepare earthenware pots is set into rotation at 100 rpm. It is in the form of a disc of mass 10 kg and a radius 0.4 m. A lump of clay (to be taken equivalent to a particle) of mass 1.6 kg falls on it and adheres to it at a certain distance x from the center. Calculate x if the wheel now rotates at 80 rpm.

Exercises | Q 22 | Page 25

Starting from rest, an object rolls down along an incline that rises by 3 in every 5 (along with it). The object gains a speed of sqrt10 m/s as it travels a distance of 5/3 m along the incline. What can be the possible shape/s of the object?

Exercises

## Balbharati solutions for Physics 12th Standard HSC Maharashtra State Board chapter 1 - Rotational Dynamics

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Concepts covered in Physics 12th Standard HSC Maharashtra State Board chapter 1 Rotational Dynamics are Rotational Dynamics, Circular Motion and Its Characteristics, Applications of Uniform Circular Motion, Vertical Circular Motion, Moment of Inertia as an Analogous Quantity for Mass, Radius of Gyration, Theorems of Perpendicular and Parallel Axes, Angular Momentum or Moment of Linear Momentum, Expression for Torque in Terms of Moment of Inertia, Conservation of Angular Momentum, Rolling Motion.

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