System of Parti...

The moment of inertia of the plate about z-axis is

Two men  '$$A$$' and '$$B$$' are standing on a plank. '$$B$$' is at the middle of the plank and '$$A$$' is at the left end of the plank. Surface of the plank is smooth. System is initially at rest and masses are as shown in figure. '$$A$$' and '$$B$$' start moving such that the position of '$$B$$' remains fixed with respect to ground and '$$A$$' meets '$$B$$'. Then the point where $$A$$ meets $$B$$ is located at

There are two particles of same mass. If one of the particles is at rest always and the other has an acceleration $$\bar{a}$$. Acceleration of center of mass is :

A ceiling fan rotates about its own axis with some angular velocity. When the fan is switched off, the angular velocity becomes $$\left (\dfrac {1}{4}\right )^{th}$$ of the original in time $$'t'$$ and $$'n'$$ revolutions are made in that time. The number of revolutions made by the fan during the time interval between switch off and rest are (Angular retardation is uniform).

If torques of equal magnitudes are applied to a hollow cylinder and a solid sphere both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry and the sphere is free to rotate about an axis passing through its center. Which of the two will acquire a greater angular speed after a given time?

Fill in the blanks.
The effect of rotation of the earth is ......... at the equator and .............. at the poles. If the earth stops rotating. the weight of a body would .......... due to the absence of .............. force.

A bar magnet of moment of inertia $$I$$ is vibrated in a magnetic field of induction $$\displaystyle 0.4\times { 10 }^{ -4 }T$$. The time period of vibration is $$12\  s$$. The magnetic moment of the magnet is $$\displaystyle 120\ { Am }^{ 2 }$$. The moment of inertia of the magnet is (in $$\displaystyle kg{ m }^{ 2 }$$) approximately:

A uniform rod of length $$l=1m$$ is kept as shown in the figure. $$H$$ is a horizontal smooth surface and $$W$$ is a vertical smooth well. The rod is release from this position. What is the angular angular acceleration of the rod just after the released?

A hoop of mass $$m$$ is projected on a floor with linear velocity $$v_{0}$$ and reverse spin $$\omega_{0}$$. The coefficient of friction between the hoop and the ground is $$\mu$$.
a. Under what condition will the hoop return back?
b. How far will it go?
c. How long will it continue to slip when its centre of mass becomes stationary?
d. What is the velocity of return?

Calculate the moment of inertia of a uniform rod of mass $$M$$ and length $$l$$ about an axis passing through an end and perpendicular to the rod. The rod can be divided into a number of mass elements along the length of the rod.