System of particles practice · Mixed difficulty

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 fly wheel of M.I $6 \times {10^{ - 2}}\,kg\,{m^2}$ is rotating with an angular velocity of $\,20\,rad\,{s^{ - 1}}$. The torque required to bring it to rest in 4 s is

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

A sphere of mass ${M}$ and radius ${R}$ is released from the top of an inclined plane of inclination $\theta$. The minimum coefficient of friction between the plane and the sphere so that it rolls down the plane without sliding is given by

If $R$ is the radius of gyration of a body of mass $M$ and radius $r$, then the ratio of its rotational to translational kinetic energy in the rolling condition is

Angular momentum is

A man standing on a platform holds weights in his outstretched arms. The system is rotated about a central vertical axis. If the man now pulls the weights inwards close to his body, then

A Mass of mass 40 kg in standing on a uniform planck of mass 60 kg lying on horizontal frictionless ice. The man walks from one end to the other end of the plank. The distance walked by the man relative to ice (given length of plank = 5 m)

The motion of the centre of mass is the result of

A ring and a disc of same mass roll without slipping along a horizontal surface with same velocity. If the K.E. of ring is 4J, then that of disc is

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

A stationary wheel starts rotating about its own axis at uniform angular acceleration $16\,rad/{s^2}$. The time taken by it to complete 77 rotations is

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

Two particles whose masses are $10 \mathrm{~kg}$ and $30 \mathrm{~kg}$ and their position vectors are $\hat{i}+\hat{j}+\hat{k}$ and $-\hat{i}-\hat{j}-\hat{k}$ respectively would have the centre of mass at

When a body is projected at an angle with the horizontal in the uniform gravitational field of the earth, the angular momentum of the body about the point of projection, as it proceeds along the path

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?

Two particles each of mass $1 {~kg}$ are located at the point having co-ordinates $(1,0,1)$ and $(1,1,0)$. The co-ordinates of the centre of mass will be

A uniform cubical box of side $a$ is placed on a rough floor and it is to be moved by applying minimum possible force $F$ at a point which is at a distance $b$ above its centre of mass. If the coeflicient of friction is $\mu=0.4$, then what is the maximum possible value of $100 \times \frac{b}{a}$ for which the box will not topple before moving?

Statement-I: A coin is placed on phonogram turn table. The motor is started, coin moves along the moving table.
Statement-II: The rotating table is providing necessary centripetal force to the coin.