System of particles practice · Medium

S-I: In rolling, all points of a rigid body have the same linear speed.
S-II: The rotational motion does not affect the linear velocity of rigid body.

A body falling vertically downwards under gravity breaks in two parts of unequal masses. The centre of mass of the two parts taken together shifts horizontally towards

A loded spring gun of mass M fires a shot of mass m with a velocity v at an angle of elevation $\theta$. The gun was initially at rest on a horizontal frictionless surface. After firing, the centre of mass of gun-shot system

A mass is revolving in a circle which is in the plane of paper. The direction of angular acceleration is

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

In free space, a shell moving with velocity $60\,m/s$ along the positive x-axis. When it passes through origin, it explodes into two pieces of mass ratio 1: 2. After the explosion, the velocity of the centre of mass is:-

What happens to the centripetal acceleration of a particle, when its speed is doubled and angular velocity is halved?

A particle is under uniform circular motion with angular momentum L. If its kinetic energy is tripled and frequency of motion is halved then new angular momentum becomes

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

Moment of inertia of an object does not depend upon

If linear density of a rod of length 3m varies as $\lambda = 2 + x$, then the position of the centre of gravity of the rod is

A body of mass ‘M’ is moving on a circular track of radius ‘r’ in such a way that its kinetic energy ‘k’ depends on the distance travelled by the body ‘s’ according to relation $k = \beta s$, where $\beta$ is a constant. The angular acceleration of the particle is

Position vector of centre of mass of two particles system is given by:

A thin uniform disc of mass $M$ and radius $R$ is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity $\omega$. Another disc of same dimension but mass $\frac{M}{2}$ is placed gently on the first disc co-axially. The angular velocity of the system now is

In the equation of angular displacement of a particle moving on a circular path is given as $\theta = 2{t^3} + 0.5,\theta$ is in radian and t in second. The angular velocity of the particle at t=2s is

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 uniform disc of mass 2 kg and radius 15 cm is revolving around the central axis by 4 $\mathrm{rad}{\mathrm{s}^{ - 1}}$. The linear momentum of disc will be

A large tray of mass ${M}$ has in it a cubical block of ice of mass ${m}$ and edge length ${L}$. The ice starts melting. The shift in the height of centre of mass of system (ice + tray) is

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

What is moment of inertia in terms of angular momentum (L) and kinetic energy (K)?

If $\alpha$ is angular acceleration, $\omega$ is angular velocity and a is the centripetal acceleration then, which of the following is true?

Statement-1: If a rod is thrown up vertically in absence of air drag, it returns back to the ground without any change in it's angular velocity.
Statement-2: In absence of any torque, the angular momentum of system is conserved.

Moment of inertia of big drop in $I$. If 8 droplets are formed from big drop, then moment of inertia of small droplet is

Find the position of centre of mass from the base of a uniform solid cone of height $20 \mathrm{~cm}$.

A car sometimes overturns while taking a turn. When it overturns, it is

Moment of inertia of a ring of mass M and radius R about an axis passing through the centre and perpendicular to the plane is $I$. What is the moment of inertia about its diameter

A constant torque acting on a uniform circular wheel changes its angular momentum from ${A_0}\,\,to\,\,\mathrm{ }7{A_0}$ in 3 s. The magnitude of average torque is

Analogue of mass in rotational motion is

A solid sphere of mass 500 g and radius 10 cm rolls without slipping with the velocity 20 cm/s. The total kinetic energy of the sphere will be

Of the two eggs which have identical sizes, shapes and weights, one is raw, and other is half boiled. The ratio between the moment of inertia of the raw to the half boiled egg bout central axis is