System of particles practice · Medium

Two homogeneous spheres A and B of masses m and 2m having radii 2a and a respectively are placed in touch. The distance of centre of mass from first sphere is

Assertion: At the centre of earth, a body has centre of mass, but no centre of gravity.
Reason: Acceleration due to gravity is zero at the centre of earth.

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 uniform heavy disc is rotating at constant angular velocity $\omega$ about a vertical axis through its centre and perpendicular to the plane of the disc. Let L be its angular momentum. A lump of plasticine is dropped vertically on the disc and sticks to it. Which will be constant

Where will be the centre of mass on combining two masses m and (M > m)

If the equation for the displacement of a particle moving on a circular path is given by $\left( \theta \right) = 2{t^3} + 0.5$, where $\theta$ is in radians and t in seconds, then the angular velocity of the particle after 2 sec from its start is

If we hollow the ball of pendulum and fill it with sand, what would be the effect of change on the center of mass?

The motion of centre of mass depends on

Two particles of masses 1 kg and 2 kg are located at ${x_1} = 0,\;{y_1} = 0\,and\,{x_2} = 1,\;{y_2} = 0$ respectively. The centre of mass of the system is at

In the absence of external torque for a body revolving about any axis, the quantity that remains constant is

Four particles of masses m,2m,3m and 4m are arranged at the corners of a parallelogram with each inside equal to a and one of the angle between two adjacent sides is ${60^0}$. The parallelogram lies in the x-y plane with mass m at the origin and 4m on the x-axis. The centre of mass of the arrangement will be located at

The principle of conservation of angular momentum, states that angular momentum

Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder P has most of its mass concentrated near its surface, while Q has most of its mass concentrated near the axis. Which statement (s) is (are) correct

A horizontal platform is rotating with uniform angular velocity around the vertical axis passing through its centre. At some instant of time a viscous fluid of mass ‘m’ is dropped at the centre and is allowed to spread out and finally fall. The angular velocity during this period

Two circular rings (of same material) are of same thickness. The diameter of first ring is twice that of second. The moment of inertia of first ring as compared to that of second is

Assertion A Moment of inertia of a circular disc of mass $M$ and radius $R$ about $X,\,Y -$ axes (passing
through its plane) and $Z -$ axis which is perpendicular to its plane were found to be ${l_x}\,\,,\,\,\,{l_y}$ and ${l_z}$
respectively. The respective radii of gyration about all the three axes will be the same.
Reason R A rigid body making rotational motion has fixed mass and shape.
In the light of the above statements, choose the most appropriate answer from the options given below.

The distance b/w the carbon atom and the oxygen atom in a carbon monoxide molecule is $1.1{A^0}$. Given mass of carbon atom is 12.a.m.u., and mass of oxygen atom is 16.a.m.u., calculate the position of the centre of mass of the carbon monoxide molecule

Angular momentum is

A stone of mass m tied to string of length $l$ is rotating along a circular path with constant speed v. The torque on the stone is

A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc

A particle moves with constant speed v along a circular path of radius r and completes the circle in time T. The acceleration of the particle is

A satellite of mass $M$ is in a circular orbit of radius $R$ about the centre of the earth. A meteorite of the same mass falling towards the earth collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same just before the collision. The subsequent motion of the combined body will be

Angular momentum is

The motion of the centre of mass is the result of

A solid homogeneous sphere is moving on a rough horizontal surface partly rolling and partly sliding. During this kind of motion of the sphere

A body is whirled in a horizontal circle of radius 20 cm. It has angular velocity of 10 rad/s. What is its linear velocity at any point on circular path

The direction of the angular velocity vector is along

The second’s hand of a watch has length 6 cm. Speed of end point and magnitude of difference of velocities at two perpendicular positions will be

The angular velocity of a wheel is 70 rad/sec. If the radius of the wheel is 0.5 m, then linear velocity of the wheel is

A solid sphere is rotating in free space. If the radius of sphere is increased keeping mass same which one of the following will not be affected?