System of particles practice · Mixed difficulty

A nonzero external force acts on a system of particles. The velocity and the acceleration of the centre of mass are found to be $v_0$ and $a_0$ at an instant $t$. It is possible that

S-I: Ratio of the distances of the centre of mass of a two particle system are in the inverse ration of their masses
S-II: The location of the centre of mass is independent of the reference frame used locate it.

When a body does not rotate or rotates with a constant angular velocity $(\omega).$ It is said to be in:

A solid cylinder of mass $M$ and radius $R$ rolls without slipping down an inclined plane of length $L$ and height $h$. What is the speed of its centre of mass when the cylinder reaches its bottom

Let $\mathrm{M}$ and $\mathrm{L}$ be the mass and length of thin uniform rod respectively. In $1^{\text {st }}$ case, axis of rotation is passing through centre and perpendicular to its length. In $2^{\text {nd }}$ case, axis of rotation is passing through one end and perpendicular to its length. The ratio of radius of gyration in first case to second case is

The centre of mass of a body is defined as the point at which the whole of its mass is supposed to be concentrated, while centre of gravity of a body is defined as the point at which whole of its weight is supposed to be concentrated then,

An equilateral triangle $A B C$ formed from a uniform wire has two small identical beads initially located at $A$. The triangle is set rotating about the vertical axis $A O$. Then the beads are released from rest simultaneously and allowed to slide down, one along $A B$ and the other along $A C$ as shown. Neglecting frictional effects, the quantities that are conserved as the beads slide down, are

The unit mass has ${r}=8 \hat{{i}}-4 \hat{{j}}$ and ${v}=8 \hat{{i}}+4 \hat{{j}}$. Its angular momentum is

Two uniform solid spheres having unequal masses and unequal radii are released from rest from the same height on a rough incline. If the spheres roll without slipping,

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A : An electric fan continues to rotate for some time after the current is switched off.

Reason R: Fan continues to rotate due to inertia of motion.

In the light of above statements, choose the most appropriate answer from the options given below.

Assertion: A solid sphere and a hollow sphere are rolling on ground with same total kinetic energies. If translational kinetic energy of solid sphere is $K$, then translational kinetic energy of hollow sphere should be greater than $K$.


Reason: In case of hollow sphere rotational kinetic energy is less than its translational kinetic energy.

What remains constant in the field of central force

A particle covers equal distances around a circular path in equal intervals of time. It has uniform nonzero rate of change of

A particle performing uniform circular motion has

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

A fly wheel is accelerated uniformly from rest and rotates through 5 rad in the first second. The angle rotated by the fly wheel in the next second, will be:

A circular disc is rotating about its natural axis with
angular velocity of 20 rad/s. A second disc of same
mass gently placed on it co-axially. If the radius of
disc is half of the radius of the first, then they will
start rotating with angular velocity of

If the net external forces acting on the system of particles is zero, then which of the following may vary?

A sphere is rotating about a diameter with constant angular acceleration $\alpha.$
Assertion (A): All the particles on the surface have same linear acceleration.
Reason (R): All the particles on the surface have same linear speed.

Angular momentum is

Moment of inertia of a uniform annular disc of internal radius $r$ and external radis $R$ and mass $M$ about an axis through its centre and perpendicular to its plane is

Three masses are placed on the x – axis, 200 g at origin, 400 g at x = 20 cm and 600 g at x = 60 cm. The distance of the centre of mass from the origin is

The moment of inertia of a circular ring of radius $15 \mathrm{~cm}$ and mass $150 \mathrm{~g}$ is _____

A binary star consists of two stars A (mass 2.2 ${M_s}$) and B (mass 11 ${M_s}$), where ${M_s}$ is the mass of the sun. They are separated by distance d and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of star B about the centre of mass is

The moment of inertia of a body about a given axis is $2.4\,kg - {m^2}$. To produce a rotational kinetic energy of 750 J, an angular acceleration of 5 rad/${s^2}$ must be applied about the axis for

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

For a body rolling along a level surface, the translational and rotational K.E are equal. The body is

Which of the following statements are correct?

1) Centre of mass of body always coincides with the centre of gravity of the body.

2) Central mass of a body is the point at which the total gravitational torque on the body is zero.

3) A couple on a body produce both translational and rotational motion in a body.

4) Mechanical advantage greater than one means that small effort can be used to lift a large load.

Two rods each having length $l$ and mass $\mathrm{m}$ joined together at point $\mathrm{B}$ as shown in figure. Then find out moment of inertia about axis passing through $\mathrm{A}$ and perpendicular to the plane of page as shown in figure.

A solid sphere of radius $R$ has its outer half removed, so that its radius becomes $(R / 2)$. Then its moment of inertia about the diameter is