A 'T' shaped object with dimensions shown in the figure, is lying on a smooth floor. A force '$\overrightarrow{\mathrm{F}}$' is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the location of P with respect to C

A wheel is rotating about an axis through its centre at 720 r.p.m. It is acted upon by a constant torque opposing its motion for 8 seconds to bring it to rest finally.The value of torque in Nm is: (given l = $\frac{24}{\mathrm{\pi }}$ kg ${\mathrm{m}}^2$)

Assertion : The speed of whirlwind in a tornado is alarmingly high.

Reason    : If no external torque acts on a body, its angular velocity remains conserved.

A circular disc A of radius r is made from an iron plate of thickness t and another circular disc B of radius 2r and thickness $\frac{\mathrm{t}}{4}$. The relation between moments of inertia ${\mathrm{I}}_{\mathrm{A}}$ and ${\mathrm{I}}_{\mathrm{B}}$ is

A stationary bomb explodes into two parts of masses 3kg and 1kg. The total KE of the two parts after explosion is 2400 J. The KE of smaller part is 

A particle of mass 2 kg located at the position $(\hat{\mathrm{i}}+ \hat{\mathrm{j}})$ m has a velocity of 2$(+\hat{\mathrm{i}} - \hat{\mathrm{j}} +\hspace{0.17em}\hat{\mathrm{k}})$ m/s. Its angular momentum about z-axis in kg-${\mathrm{m}}^2/\mathrm{s}$ is :

A cylinder of mass 'M' is suspended by two strings wrapped around it as shown. The acceleration 'a' and the tension T when the cylinder falls and the string unwinds itself are, respectively,
             

An automobile engine develops 100 kW when rotating at a speed of 1800 rev/min. What torque does it deliver ?

In an orbital motion, the angular momentum vector is 

A particle of mass m moves with a constant velocityalong 3 different paths, DE, OA and BC. Which of the following statements is not correct about its angular momentum about point O?

A sphere is rolling down a plane of inclination $\theta$ to the horizontal.  The acceleration of its centre down the plane is 

A body at rest breaks into two pieces of equal masses.  The parts will move

A bob of mass m attached to an inextensible string of length l is suspended from verticle support.  The bob rotates in a horizontal circle with an angular speed $\mathrm{\omega } \mathrm{rad}/\mathrm{s}$ about the vertical.  About the point of suspension.

In free space, a rifle of mass M shoots a bullet of mass m at a stationary block of mass M at a distance D away from it. When the bullet has moved through a distance d towards the block, the centre of mass of the bullet - block system is at a distance of

Blocks A and B are resting on a smooth horizontal surface given equal speeds of 2 m/s in the opposite sense as shown in the figure.

At t = 0, the position of blocks are shown, then the coordinates of centre of mass at t = 3s will be 

A wheel is at rest. Its angular velocity increases uniformly and becomes 80 rad/s after 5 s. The total angular displacement is 

A force $-\mathrm{F}\hat{\mathrm{k}}$ acts on O, the origin of the coordinate system. The torque at the point (1, -1) will be:

Moment of inertia of an object does not depend upon

A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its center and perpendicular to its plane with an angular velocity $\omega$. Another disc of the same dimensions but of mass $\frac{1}{4}M$ is placed gently on the first disc co-axially.The angular velocity of the system will be:

When a ball of mass = 5kg hits a bat with a velocity = 3 m/s, in positive direction and it moves back with a velocity = 4 m/s, find the impulse in SI units

When a torque acting upon a system is zero, then which of the following will be constant 

Consider a system of two particles having masses ${\mathrm{m}}_1 \mathrm{and} {\mathrm{m}}_2$. If the particle of mass ${\mathrm{m}}_1$ is pushed towards the center of mass of particles through a distance, by what distance would be the particle of the mass ${\mathrm{m}}_2$ move so as to keep the center of mass of particles at the original position?

The rotational KE of a body is E and its moment of inertia is I. The angular momentum is 

If the linear density of a rod of length 3m varies as $\lambda$=2+x, then the position of the center of mass of the rod is at a distance of:

A flywheel is in the form of a uniform circular disc of radius 1 m and mass 2 kg. The work which must be done on it to increase its frequency of rotation from 5 rev ${\mathrm{s}}^{-1}$ to 10 rev ${\mathrm{s}}^{-1}$ is approximately

A particle of mass m has momentum p. it's kinetic energy will be 

A constant torque acting on a uniform circular wheel changes its angular momentum from ${\mathrm{A}}_0$ to $4 {\mathrm{A}}_0$ in 4s. The magnitude of this torque is 

Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc D${}_1$ has 2 kg mass and 0.2 m radius and initial angular velocity of 50 rad s${}^{-1}$. Disc D${}_2$ has 4 kg mass, 0.1 m radius and initial angular velocity of 200 rad s${}^{-1}$. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in rad.s${}^{-1}$) of the system is

A body rolls down an inclined plane without slipping. The fraction of total energy associated with its rotation will be

$$\begin{gathered} 1. {\mathrm{K}}^2+ {\mathrm{R}}^2 \\ 2. \frac{{\mathrm{K}}^2}{{\mathrm{R}}^2} \\ 3. \frac{{\mathrm{K}}^2}{{\mathrm{K}}^2+ {\mathrm{R}}^2} \\ 4. \frac{{\mathrm{R}}^2}{{\mathrm{K}}^2+ {\mathrm{R}}^2} \end{gathered}$$

Where k is radius of gyration of the body about an axis passing through centre of mass and R is the radius of the body. 

A mass of 100 g strikes the wall with speed 5 m/s at an angle as shown in figure and it rebounds with the same speed. If the contact time is $2\times {10}^{-3}$ s, what is the force applied on the mass by the wall