System of particles practice · Medium

A uniform solid sphere of mass M and radius R is pulled on a horizontal plane by a horizontal force F acting through its mass centre. Assuming rolling without slipping what is the angular acceleration of the sphere?

Assertion: Moment of inertia depends on the axis
of rotation and the nature of distribution of the
mass of the body.
Reason: Moment of inertia is the rotational inertia
of the body.

The torque on a body is zero. Which of the following should not change?

Assertion: The centre of mass of system of $n$ particles is the weighted average of the position vector of the $n$ particles making up the system.
Reason: The position of the centre of mass of a system is independent of coordinate system.

A swimmer while jumping into water from a height easily forms a loop in the air, if

Assertion: The torque due to a force always acts perpendicular to the force vector.
Reason: $\vec{\tau}=\vec{r} \times \overrightarrow{{F}}$

A uniform thin rod of mass $M$ and length $L$ is standing vertically along the $Y$-axis on a smooth horizontal surface with its lower end at origin $(0,0)$. A slight disturbance at $t=0$ causes the lower end to slip on smooth surface along the positive X-axis and the rod starts falling. The path followed by the centre of mass of the rod during its fall is a/an.

Torque applied on a particle is zero, then its angular momentum will be

Angular momentum of a body is defined as the product of

From a circular disc of radius R and mass 4m, a small disc of radius $\frac{R}{2}$ is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre is

Assertion: A man sitting on a rolling table, when he stretches his arms horizontally, his speed is reduced.
Reason: Principle of conservation of angular momentum is applicable in this situation.

Two atoms of oxygen are located at $r_1$ and $r_2$. Their centre of mass is at

A loop of radius 3 meter and weighs $150 \mathrm{~kg}$. It rolls along a horizontal floor so that its centre of mass has a speed of 15 $\mathrm{cm} / \mathrm{sec}$. How much work has to be done to stop it

For a given mass and size, moment of inertia of a solid disc is:

Two spheres of masses 2M and M are initially at rest at a distance R apart. Due to mutual force of attraction, they approach each other. When they are at separation R/2, the acceleration of the centre of mass of spheres would be

A solid object is rotating freely without experiencing any external torque. In this case

Assertion: The total distance moved by any point on the periphery of a wheel of radius $R$ along the surface in one revolution is $2 \pi R.$
Reason: In rolling motion of a wheel, every point on its periphery comes in contact with the surface once in one revolution.

(A): Value of radius of gyration of a body depends on axis of rotation.
(R): Radius of gyration is root mean square distance of particle of the body from the axis of rotation.

Two particles of mass ${m_1}$ and ${m_2}\,({m_1} > {m_2})$ attract each other with a force inversely proportional to the square of the distance between them. If the particles are initially held at rest and then released, the centre of mass will

The two persons of masses 55 kg and 65 kg respectively, are at at opposite ends of a boat. The length of the boat is 30 m and weight 100 kg. The 55 kg man walkup to the 65 kg man and its with him. If the boat is in still water the centre of mass of the system shifts by

A solid sphere is under pure rolling on a table. The fraction of its total kinetic energy associated with rotation is

Assertion: If ice caps of the pole melts, the day length will shorten.
Reason: Ice flows towards the equator and decreases the moment of inertia of the earth and hence increases the frequency of rotation of the earth.

A metre stick is placed vertically at the origin on a frictionless surface. A gentle push in $+x$-direction is given to the top most point of the rod. When it has fallen completely, the $x$-coordinate of centre of rod is at

A cylinder is rolling over a surface. Which points on it move rectilinearly?

A solid sphere is rotating about a diameter at an angular velocity $\omega$. If it cools so that its radius reduces to $\frac{1}{n}$ of its original value, its angular velocity becomes

A closed tube partly filled with water lies in a horizontal plane. If the tube is rotated about perpendicular bisector, the moment of inertia of the system

Assertion: There are very small sporadic changes in the period of rotation of the earth.
Reason: Shifting of large air masses in the earth's atmosphere produce a change in the moment of inertia of the earth causing its period of rotation to change.

A body of radius $R$ and mass $M$ is rolling horizontally without slipping with speed $v$, it then rolls up a hill to a maximum height $h$. If $h=3 v^2 / 4 \mathrm{~g}$, what is the moment of inertia of the body?

Angular momentum is

When a disc rotates with uniform angular velocity, which of the following is not true?