Questions in rotational-motion

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Three identical spheres, each of mass 1 kg are placed touching each other with their centres on a straight line. Their centres are marked K, L and M respectively. The distance of centre of mass of the system from K is
Two particles of masses 1 kg and 3 kg move towards each other under their mutual force of attraction. No other force acts on them. When the relative velocity of approach of the two particles is 2m/s, their centre of mass has a velocity of 0.5 m/s. When the relative velocity of approach becomes 3 m/s, the velocity of the centre of mass is
In rotational motion of a rigid body, all particle move with
The angular speed of a fly–wheel making 120 revolution/minute is
A flywheel gains a speed of 540 r.p.m. in 6 sec. Its angular acceleration will be
A car is moving at a speed of 72 km/hr. the diameter of its wheels is 0.5 m. If the wheels are stopped in 20 rotations by applying brakes, then angular retardation produced by the brakes is
A wheel is rotating at 900 r.p.m. about its axis. When the power is cut-off, it comes to rest in 1 minute. The angular retardation in $radian/s^2$ is
A particle B is moving in a circle of radius a with a uniform speed u. C is the centre of the circle and AB is diameter. The angular velocity of B about A and C are in the ratio
Two particles having mass 'M' and 'm' are moving in circular paths having radii $R$ and $r$. If their time periods are same then the ratio of their angular velocities will be
A body is in pure rotation. The linear speed v of a particle, the distance r of the particle from the axis and angular velocity $\omega $ of the body are related as $\omega =\frac{v}{r}$, thus

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