System of particles practice · Medium

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

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?

(A): When couple acting on a body moment of the couple does not depends on the point about which moments are measured.
(R): When a couple acts on a body it is in translational equilibrium.

A couple produces

Assertion: When a body dropped from a height explodes in mid air, its centre of mass keeps moving in vertically downward direction.
Reason: Explosion occur under internal forces only. External force is zero.

A diver having a moment of inertia of $6.0 \mathrm{~kg}-\mathrm{m}^2$ about an axis through its centre of mass rotates at angular speed of $2 \mathrm{~rad} / \mathrm{s}$ about this axis. If he folds his hands and feet to decrease the moment of inertia to $5.0 \mathrm{~kg}-\mathrm{m}^2,$ what will be the new angular speed?

Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities ${\omega _1}\mathrm{\; and\; }{\omega _2}.$ They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is

Moment of inertia (MI) of four bodies, having same mass and radius, are reported as ${I_1} = MI$ of thin circular ring about its diameter,
${I_2} = MI$ of circular disk about an axis perpendicular to the disk and going through the centre,
${I_3} = MI$ of solid cylinder about its axis and ${I_4} = MI$ of solid sphere about its diameter. Then,

If an object starts from rest and covers angle of $60 \mathrm{~rad}$ in $10 \mathrm{~s}$ in circular motion, then magnitude of its angular acceleration will be

A star of mass twice the solar mass and radius $10^6 \mathrm{~km}$ rotates about its axis with an angular speed of $10^{-6} \mathrm{~rad} \mathrm{~s}^{-1}$. What is the angular speed of the star when it collapses (due to inward gravitational force) to a radius of $10^4 \mathrm{~km}$? Solar mass $1.99 \times 10^{30} \mathrm{~kg}$.

The angular momentum of a system of particles is not conserved

A particle is moving on a circle of radius $R$ such that at every instant the tangential and radial accelerations are equal in magnitude. If the velocity of the particle be ${v}_0$ at ${t}=0$, the time for the completion of half of first revolution will be

What is the moment of inertia of solid sphere of density $\rho$ and radius R about its diameter?

Assertion: The condition of equilibrium for a rigid body is- Translational equilibrium : $\sum \overrightarrow{\mathrm{F}}=0$, (i.e. sum of all external forces equal to zero.) Rotational equilibrium: $\sum \vec{\tau}=0$, (i.e. sum of all external forces equal to zero.)
Reason: A rigid body must be in equilibrium under the action of two equal and opposite forces.

Assertion: The centre of mass of a system of two particles of unequal masses is closer to the heavier particle.
Reason: The centre of mass of a system of two particles divides the distance between the particles in the inverse ratio of their masses.

The centre of mass of a body

Two racing cars of masses ${m_1}\,and\,{m_2}$ are moving in circles of radii ${r_1}\,and\,{r_2}$ respectively. Their speeds are such that each makes a complete circle in the same duration of time t.The ratio of the angular speed of the first to the second car is

(A): The hard boiled egg and raw egg can be distinguished on the basis of spinning of both.
(R): The moment of inertia of hard boiled egg is more as compare to raw egg.

If the torque of the rotational motion by zero,
then the constant quantity will be

A solid sphere, hollow sphere, solid cylinder, hollow cylinder and ring each of mass $M$ and radius $R$ are simultaneously released at rest from top of incline and allowed to roll down the incline. The angular acceleration is maximum for

What is the angular velocity of earth

The moment of inertia $(I)$ of a sphere of radius $R$ and mass $M$ is given by