System of particles practice · Mixed difficulty

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

When a sphere rolls down an inclined plane, then identity the correct statement related to the work done by friction force

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?

A solid sphere and a spherical shell roll down an incline from same height the ratio of times taken by them is

Two blocks of masses 10 kg and 4 kg connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of $14\mathrm{\;m}{\mathrm{s}^{ - 1}}$ to the heavier block in the direction of the lighter block. The velocity of the centre of mass is

The rotors velocity of a helicopter engine changes from $300 \,\mathrm{rev} / \mathrm{min}$ to $110 \,\mathrm{rev} / \mathrm{min}$ in 2 minutes. How long does the rotor blades take to stop

Two circular iron discs are of the same thickness. The diameter of A is twice that of B. The moment of inertia of A as compared to that of B is

Two discs having moment of inertia $\mathrm{I}_1$ and $\mathrm{I}_2$ are made from same material have same mass. Their thickness and radii are $\mathrm{t}_1, \mathrm{t}_2$ and $\mathrm{R}_1, \mathrm{R}_2$ respectively. The relation between moment of inertia of each disc about an axis passing through its centre and perpendicular to its plane and its thickness is

A motor is rotating at a constant angular velocity of 600 rpm. The angular displacement per second is

The correct relation between moment of inertial $I$, radius of gyration $K$ and mass $M$ of the body is:

Two particles of masses 5 kg and 3 kg moves with velocity $2\,m{s^{ - 1}}$ and $4\,m{s^{ - 1}}$ in the same direction. Find the velocity of centre of mass of the system of two particles is

A wheel is rotating at $900 \mathrm{rpm}$ about its axis. When power is cut-off, it comes to rest in $1 \mathrm{~min}$. The angular retardation (in $\mathrm{rad} \mathrm{s}^{-2}$ ) is

Moment of inertia of a solid sphere about its diameter is ' $\mathrm{I}$ '. It is then casted into 27 small sphere of same diameter. The moment of inertia of each new sphere is

A wheel is rotating at $480 \mathrm{~rpm}$. Find the magnitude of angular acceleration required to stop the wheel in 8 seconds?