System of particles practice · Mixed difficulty

Assertion(A): If a particle moves with a constant velocity, then angular momentum of this particle about any point remains constant.

Reason(R): Angular momentum has the units of Planck's constant.

The conservation of angular momentum demands that

Assertion: Torque on a body can be zero even if there is a net force on it.

Reason: Torque and force on a body are always perpendicular.

An automobile engine develops ${10^5}\,\mathrm{W}$ power when rotating at an angular speed of 900 rad/minute. The instantaneous torque delivered by the engine is

A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first 2 sec, it rotates through an angle ${\theta _1}$. In the next 2 sec, it rotates through an additional angle ${\theta _2}$. The ratio of ${\theta _2}/{\theta _1}$ is

A solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is –

The radius of gyration of a sphere of radius $R$ about a certain axis is also $R.$ The distance of this axis from the center of the sphere is:

A body is under the action of two equal and oppositely directed forces and the body is rotating with constant non-zero angular acceleration. Which of the following cannot be the separation between the lines of action of the forces?

Two loops $P$ and $Q$ are made from a uniform wire. The radii of $P$ and $Q$ are $r_1$ and $r_2$ respectively, and their moments of inertia are $I_1$ and $I_2$ respectively. If $I_2=4 I_1$, then $\frac{r_2}{r_1}$ equals -

A solid sphere and hollow sphere of same mass and radius rotate about their diameter with same rotational kinetic energy. If torques of equal magnitude are applied on them, ratio of their angular displacement before they are bought to rest.

A particle of mass 1 kg is projected with an initial velocity 10 $\mathrm{m}{\mathrm{s}^{ - 1}}$  at an angle of projection ${45^0}$ with the horizontal. The average torque acting on the projectile, between the time at which it is projected and the time at which it strikes the ground, about the point of projection in newton-metre is

A particle of mass 1 kg is projected with an initial velocity 10 $\mathrm{m}{\mathrm{s}^{ - 1}}$  at an angle of projection ${45^0}$ with the horizontal. The average torque acting on the projectile, between the time at which it is projected and the time at which it strikes the ground, about the point of projection in newton-metre is

A uniform sphere of mass 250 g rolls without slipping on a plane horizontal surface with its centre moving at a speed of 5 cm/s. Its kinetic energy is

An ice stacker spins at $3\, \pi\, rad \, s^{-1}$with her arms extended. If her moment of inertia with arms folded is $75 \%$ of that with arms extended, her angular velocity when she folds her arms is

If a body of moment of inertia $2\, {~kg} \,{~m}^2$ revolves about its own axis making 2 rotations per second, then its angular momentum (in ${J} {s}$ ) is

A constant torque acting on a uniform circular wheel changes its angular momentum from ${A_0}$ to $4{A_0}$ in 4 seconds. The magnitude of this torque is

A fly-wheel of mass $25 \mathrm{~kg}$ has a radius of $0.2 \mathrm{~m}$. It is making $240 \mathrm{~rpm}$. What is the torque necessary to bring to rest in $20 \mathrm{~s}$?

The instantaneous angular position of a point on a rotation wheel is given by the equation $\theta (t) = 2{t^3} - 6{t^2}$. The torque on the wheel becomes zero at

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

Three identical sphere lie at rest along a line on a smooth horizontal surface. The separation between any two adjacent spheres is L. The first sphere is moved with a velocity u towards the second sphere at time t=0. The coefficient of restitution for collision between any two blocks is 1/3. Then choose the correct statement

Assertion: If linear momentum of a particle is constant, then its angular momentum about any point will also remain constant.

Reason: Linear momentum remains constant, if ${F}_{\text {net}}=0$ and angular momentum remains constant if $\tau_{\text {net}}=0$.

A hollow sphere and a solid sphere, of equal mass and equal radii roll down without slipping on an inclined plane. If the torque experienced by the hollow sphere and solid sphere are $\tau_{\mathrm{H}}$ and $\tau_{\mathrm{S}}$ respectively, then

Assertion: When a sphere is rolls freely on a horizontal table, it slows down and eventually stops.

Reason: When the sphere rolls on the table, both the sphere and the surface deform near the contact. As a result, the normal force does not pass through the centre and provide an angular deceleration.

We have two spheres, one of which is hollow and other is solid. They have identical mass and moment of inertia about its tangent. The ratio of their radii is given by

A hollow sphere of mass $M$ and radius $R$ is in pure rolling on the horizontal rough surface. The ratio of rotational kinetic energy to the total kinetic energy of the hollow sphere will be

When a ceiling fan is switches on it makes 10 revolutions in the first 3 seconds. Assuming a uniform angular acceleration, how many rotation it will make in the next 3 seconds.

Two particles of equal masses have velocities ${v}_1=4 \hat{i}{\mathrm{~ms}}^{-1}$ and ${v}_2=4 \hat{{j}} \mathrm{~ms}^{-1}.$ First particle has an acceleration $a_1=(2 \hat{i}+2 \hat{j}) \mathrm{ms}^{-2},$ while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a path of:

A hollow sphere and solid sphere rolls on a horizontal surface without slipping with same linear velocity. If both has same mass and radius and total kinetic energy of hollow sphere is $15 \mathrm{~J}$ then total kinetic energy of the solid sphere is

The highest moment of inertia if all the objects have same mass and same radius is of

A body of mass 36 kg moves from one end to other end of a boat of mass 72 kg in still water. If the length of the boat is 2.7 m, the displacement of the boat is