System of particles practice · Mixed difficulty

A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then maximum acceleration down the plane is for (no rolling)

In uniform circular motion

Centre of mass for a uniform semi-circular ring will be at (from centre)

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

Moment of inertia of a uniform circular disc about a diameter is $\frac{I}{2}$. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be

The angular speed of fly wheel moving with uniform angular acceleration changes from 1200 rpm to 3120 rpm in 16 seconds. The angular acceleration in $\mathrm{rad/}{\mathrm{s}^2}$ is:

The principle used by a gymnast to increase the number of somersaults, is law of conservation of

Choose the correct statement about the centre of mass (CM) of a system of two particles

A straight thin uniform rod of length 4L and mass 4M is bent into a square. Its M.I about one side is

The motor of an engine is rotating about its axis with an angular velocity of $100 \mathrm{~rpm}$. It comes to rest in $15 \mathrm{~s}$, after being switched OFF. Assuming constant angular deceleration, what are the numbers of revolutions made by it before coming to rest?

Two bodies of masses 2 kg and 4 kg are moving with velocities 20 $\mathrm{m}{\mathrm{s}^{ - 1}}$ and 10 $\mathrm{m}{\mathrm{s}^{ - 1}}$ towards each other due to mutual gravitation attraction. What is the velocity of their centre of mass?

Two identical solid cylinders run a race starting from rest at the top of an inclined plane. If one cylinder slides and the other rolls:

Angular momentum is conserved

Assertion: A satellite is orbiting around a planet then its angular momentum is conserved.

Reason: Linear momentum conservation leads to angular momentum conservation.

A hollow sphere of mass $2 \mathrm{~kg}$ and radius $2 \mathrm{~cm}$ is rolling down a rough incline of inclination $\theta=30^{\circ}$. The acceleration of its centre down the incline is $\left(g=10 \mathrm{~m} / \mathrm{s}^2\right)$

A circular disc ' $X$ ' of radius ' $R$ ' made from iron plate of thickness ' $t$ ' has moment of inertia ' $I_x$ ' about an axis passing through the centre of disc and perpendicular to its plane. Another disc ' $Y$ ' of radius ' $3 R$ ' made from an iron plate of thickness $\left(\frac{t}{3}\right)$ has moment of inertia ' $I$ ', about the axis same as that of disc $X$. The relation between $I_x$ and $I_y$ is

Assertion: If the head of a right-handed screw rotates with the body, the screw advances in the direction of the angular velocity.
Reason: For rotation about a fixed axis, the angular velocity vector lies along the axis of rotation.

A solid sphere of radius $R$ is placed on a smooth horizontal surface. A horizontal force ' $F$ ' is applied at height ' $h$ ' from the lowest point. For the maximum acceleration of the centre of mass, which is correct?

Consider the following statements and choose the correct option
I) Position vector of centre of mass of two particles of equal mass is equal to the position vector of either particle
II) Centre of mass is always at the midpoint of the line joining two particles
III) Centre of mass of a body can lie where there is no mass

Assertion: A sphere cannot roll on a smooth inclined surface.
Reason: The motion of a rigid body which is pivoted or fixed in some way is rotation.

If an angular momentum of a body of fixed M.I. increases by $50 \%$, its kinetic energy of rotation increases by:

A uniform metallic rod rotates about its perpendicular bisector with constant angular speed. If it is heated uniformly to raise its temperature slightly, then

A large number of particles are placed around the origin, each at a distance $R$ from the origin. The distance of the centre of mass of the system from the origin is

A fan is moving around its axis. What will be its motion regarded as?

The momentum of a system is defined

Assertion: For a system of particles under central force field, the total angular momentum is conserved.
Reason: The torque acting on such a system is zero.

The position of particle is given by $\overrightarrow r = \hat i + 2\hat j - \hat k$ and momentum $\overrightarrow p = 3\hat i + 4\hat j - 2\hat k.$ The angular momentum is perpendicular to

A particle moves in a force field given by: $\vec{F}=\hat{r} F(r)$, where $\hat{r}$ is a unit vector along the position vector $\vec{r}$, then which is true?

A spherical shell has mass $M$ and radius $R$. Moment of inertia about its diameter will be

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