A small mass attached to a string rotates on a frictionless table top as shown. If the tension on the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2, the kinetic energy of the mass will

Three-point masses 'm' each, are placed at the vertices of an equilateral triangle of side a. Moment of inertia of the system about axis COD is-

A particle is moving in a circular orbit with constant speed. Select wrong alternate

An ABC is a right-angled triangular plate of uniform thickness. The sides are such that AB > BC. As shown in the figure \(I_1,I_2\)  and \(I_3\) are moments of inertia about AB, BC and AC respectively. Which of the following relation is correct?

One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moment of inertia about their diameters are respectively I_A and I_B such that

A couple produces:                                                               [NTSE 1995; CBSE PMT 1997; DCE 2004]

A particle of mass 1 kg is kept at (1m, 1m, 1m). The moment of inertia of this particle about z-axis would be

One quarter sector is cut from a uniform circular disc of radius R.  This sector has mass M.  It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc.  Its moment of inertia about the axis of rotation is [IIT-JEE (Screening) 2001]

A wheel is rotating at the rate of 33 rev/min.  If it comes to stop in 20 s. Then, the angular retardation will be

A ball hits the floor and rebounds after an inelastic collision. In this case

A solid sphere is rotating about a diameter at an angular velocity $\omega$.  If it cools so that its radius reduces to $\frac{1}{n}$ of its  original value, its angular velocity becomes [MP PMT 2006]

A horizontal platform is rotating with uniform angular velocity around the vertical axis passing through its centre. At some instant of time a viscous fluid of mass 'm' is dropped at the centre and is allowed to spread out and finally fall. The angular velocity during this period

For L = 3.0 m,the total torque about pivot A provided by the forces as shown in the figure is:

For the same total mass, which of the following will have the largest moment of inertia about an axis passing through the centre of gravity and perpendicular to the plane of the body?

The radius of gyration of a uniform rod of length L about an axis passing through its centre of mass is

Two uniform, thin, identical rods, each of mass M and length l are joined together to form a cross. What will be the moment of inertia of the cross about an axis passing through the point at which the two rods are joined and are perpendicular to the plane of the cross?

If the linear momentum is increased by 50%, the kinetic energy will increase by

If the kinetic energy of a body increases by 0.1%, the percent increase of its momentum will be 

A solid cylinder and a hollow cylinder, both of the same mass and same external diameter are released from the same height at the same time on an inclined plane. Both roll down without slipping. Which one will reach the bottom first?

A man is sitting on a rotating table with his arms stretched outwards.  When he suddenly folds his arms inside, then

A body of mass M and radius R is rolling horizontally without slipping with speed v.  It then rolls up a hill to a maximum height h.  If $h=\frac{5v^2}{6g}$, what is the M.I of the body?

One projectile moving with velocity v in space, gets burst into 2 parts of masses in the ratio 1:3.  The smaller part becomes stationary.  What is the velocity of the other part?

One circular ring and one circular disc both having the same mass and radius. The ratio of their moments of inertia about the axes passing through their centres and perpendicular to planes will be

A wheel of radius R rolls on the ground with a uniform velocity v. The velocity of topmost point relative to the bottommost point is

The figure shows a uniform solid block of mass M and edge lengths a, b and c. Its M.O.I. about an axis through one edge and perpendicular (as shown) to the large face of the block is 

The moment of inertia of a cube of mass m and side a about one of its edges is equal to

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

A constant torque of 1000 N-m turns a wheel of moment of inertial 200 $\mathrm{kg}-{\mathrm{m}}^2$ about an axis through its centre. Its angular velocity after 3 s is

Point masses ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$ are placed at the opposite ends of a rigid of length L and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point P on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity ${\mathrm{\omega }}_0$ is minimum is given by

$$\begin{gathered} 1. \mathrm{x} =\frac{{\mathrm{m}}_1}{{\mathrm{m}}_2}\mathrm{L} \\ 2. \mathrm{x} = \frac{{\mathrm{m}}_2}{{\mathrm{m}}_1}\mathrm{L} \\ 3. \mathrm{x} = \frac{{\mathrm{m}}_2\mathrm{L}}{{\mathrm{m}}_1+ {\mathrm{m}}_2} \\ 4. \mathrm{x} = \frac{{\mathrm{m}}_1\mathrm{L}}{{\mathrm{m}}_1+ {\mathrm{m}}_2} \end{gathered}$$

A circular disc of radius r has a uniform thickness.  A circular hole of diameter equal to the radius of the disc has been cut out as shown.  The centre of gravity of the remaining disc lies on the diameter of the disc at a distance x to the left of the centre of the original disc.  The value of x is