System of particles practice · Mixed difficulty

What remains constant in the field of central force

A uniform metal rod is bent into L shape with the bent arms at $90^\circ$ to each other. The distance of the centre of mass from the bent point is

If all of a sudden the radius of the earth decreases, then

The linear acceleration of the centre of gravity of a solid sphere which rolls down without slipping over an inclined plane with an angle of inclination ${30^0}$ is

STATEMENT-1: If there is no external torque on a body about its center of mass, then the velocity of the center of mass remains constant.

STATEMENT-2: The linear momentum of an isolated system remains constant.

A particle of mass m is circulating on a circle of radius r having angular momentum L, then the centripetal force will be

In a bicycle the radius of rear wheel is twice the radius of front wheel. If ${r_F}\,and\,{r_r}$ are the radius, ${v_F}\,and\,{v_r}$, are speeds of top most points of wheel, then

The radius vector and linear momentum are respectively given by vector $\mathrm{2\hat i} + 2\mathrm{\hat j} + \mathrm{\hat k \,\,and\,\, 2\hat i} - 2\mathrm{\hat j} + \mathrm{\hat k}$  Their angular momentum is

In an elastic head on collision between two particles

The centre of mass of a body

One circular ring and one circular disc, both are having the same mass and radius. The ratio of their moments of inertia about the axes passing through their centres and perpendicular to their planes, will be

If a force $10\hat i + 15\hat j + 25\hat k$ acts on a system and gives an acceleration $2\hat i + 3\hat j - 5\hat k$ to the centre of mass of the system, the mass of the system is

The angular displacement of a particle is 5 rad. Then its angular velocity at $t = 10\,sec$ is $\left( {rad{s^{ - 1}}} \right)$

A small object of mass m is attached to a light string which passes through a hollow tube. The tube is hold by one hand and the string by the other. The object is set into rotation in a circle of radius R and velocity v. The string is then pulled down, shortening the radius of path of $r$. What is conserved

A body of moment of inertia ${4 kgm^2}$ rotating with an angular speed of 4 rad/s has the 4 x J of kinetic energy. Determine the value of x.

A uniform solid sphere of diameter 0.2 m and mass 10 kg is rotated about its diameter with an angular velocity of $2\,rad\,{s^{ - 1}}$. Then its angular momentum in $kg\,{m^2}\,{s^{ - 1}}$ is

Which of the following statements are incorrect about centre of mass?
I) Centre of mass can coincide with geometrical centre of a body
II) Centre of mass of a system of two particles does not always lie on the line joining the particles
III) Centre of mass should always lie on the body

A fan is making 600 revolutions per minute. If after some time it makes 1200 revolutions per minute, then increase in its angular velocity is

A constant torque of 500 N-m turns a wheel of moment of inertia $100\,kg - {m^2}$ about axis through its centre. Its angular velocity after 6 sec is

A disk and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?

A thick straight wire of length $4\pi \,m\,$ is fixed at its midpoint and the bent in the form of a circle. The shift in its centre of mass is

A curved road of diameter 1.8 km is banked so that no friction is required at a speed of $30\;\mathrm{m}{\mathrm{s}^{ - 1}}$. What is the banking angle?

A bomb travelling in a parabolic path under gravity, explodes in mid air. The centre of mass of fragments will move

There are two identical balls of same material, one being solid and the other being hollow. How will you distinguish them without weighing?

The centre of mass of a system cannot change its state of motion, unless there is external force acting on it. Yet the internal force of the brakes can bring a car to rest. Then

A stone is swinging in a horizontal circle 0.8 m in diameter, at 30rev/min. A distant light causes a shadow of the stone to be formed on a nearby wall. What is the amplitude of the motion of the shadow? What is the frequency?

Two objects of mass 100 g and 400 g posses velocity $5\hat i\,m/s$ and $3\hat i + 3\hat j\,m/s$ respectively. The velocity of their centre of mass in m/s is

A uniform thin rod of mass $M$ and length $L$ is standing vertically along the $Y$-axis on a smooth horizontal surface with its lower end at origin $(0,0)$. A slight disturbance at $t=0$ causes the lower end to slip on smooth surface along the positive X-axis and the rod starts falling. The path followed by the centre of mass of the rod during its fall is a/an.

The moment of interia of a rod about its perpendicular bisector is $I$. When the temperature of the rod is increased by $\Delta T$, the increase in the moment of inertia of the rod about same axis is (Here, $\alpha$ is the coefficient of linear expansion o the rod) :

A non-zero external force acts on a systems of particles. The velocity and acceleration of the centre of mass are found to be ${v_0}\,and\,{a_0}$ at an instant t. It is possible that