Maharashtra Board Solutions for Chapter: Rotational Dynamics, Exercise 3: Exercises

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 particle of mass $1 \mathrm{kg}$, tied to a $1.2 \mathrm{m}$ long siring is whirled to perform vertical circular motion, under gravity. Minimum speed of a particle is $5 \mathrm{m}/\mathrm{s}$. Consider following statements.

P) Maximum speed must be $5\sqrt{5} \mathrm{m}/\mathrm{s}$.

Q) Difference between maximum and minimum tensions along the string is $60 \mathrm{N}$. Select correct option.

Select the correct option.

Select correct statement about the formula (expression) of moment of inertia (MI) in terms of mass M of the object and some of its distance parameter/s, such as R, L, etc.

In a certain unit, the radius of gyration of a uniform disc about its central and transverse axis is $\sqrt{2.5}$. Its radius of gyration about a tangent in its plane (in the same unit) must be

Consider 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? 

 A metallic ring of mass $1 \mathrm{kg}$ has moment of inertia $1 \mathrm{kg} {\mathrm{m}}^2$ 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. 

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

Starting from rest, an object rolls down along an incline that rises by 3 units in every 5 units (along it). The object gains a speed of $\sqrt{10} \mathrm{m}/\mathrm{s}$ as it travels a distance of $\frac{5}{3}\mathrm{m}$ along the incline. What can be the possible shape/s of the object?