List of top Physics Questions on System of Particles & Rotational Motion asked in KEAM

The analogy between linear motion and rotational motion are given. The FALSE one is:
The collision in which the two colliding particles move together after collision is called:
In the electron emission process, \( _{Z}^{A}X \rightarrow _{Z+1}^{A}Y + e^{-} + \bar{\nu} \), the particle \( q \) emitted along with the electron is:
A wheel is rolling on a plane surface. A point on the rim of the wheel at the same level as the Centre has a speed of 4m/s. The speed of the Centre of the wheel is:

A ring of radius 1.75 m stands vertically. A small sphere of mass 1kg rolls on the inside of this ring without slipping. If it has a velocity of 10m/s at the bottom of the ring,then its velocity when it reaches the top is:(Take g=10 m/s2)

Two identical solid spheres,each of radius 10cm,are kept in contact. If the mass of inertia of this system about the tangent passing through the point of contact is 0.14 kg.\(m^2\) Then mass of each sphere is:

A uniform thin rod of mass 3kg has a length of 1m. If a point mass of 1kg is attached to it at a distance of 40cm from its center,the center of mass shifts by a distance of: 
A particle has the position vector ${r} = \hat{i} - 2\hat{j } + \hat{k}$ and the linear momentum ${p} = 2\hat{i} - \hat{j} + \hat{k}$. Its angular momentum about the origin is
A carpet of mass $m$ made of inextensible material is rolled along its length in the form of a cylinder of radius $r$ and kept on a rough floor. The decrease in the potential energy of the system, when the carpet is unrolled to a radius $\frac{r}{2}$ without sliding is $(g=$ acceleration due to gravity)
A system consisting of two masses connected by a massless rod lies along the x-axis. A 0.4 kg mass is at a distance x = 2 m while a 0.6 kg mass is at a distance x = 7 m. The x-coordinate of the center of mass is
A solid sphere and a hollow sphere, both of the same size and same mass roll down an inclined plane .Then
A solid cylinder rolls down an inclined plane of height 3 m and reaches the bottom of plane with angular velocity, of 2 $ \sqrt {2} rads ^{-1} $ . The radius of cylinder must be (Take g = 10 $ ms ^{-2}$ )
When a ceiling fan is switched off, its angular velocity reduces to half its initial value after it completes 36 rotations. The number of rotations it will make further before coming to rest is (Assuming angular retardation to be uniform)
A thin circular ring of mass m and radius R is rotating about its axis perpendicular to the plane of the ring with a constant angular velocity $\omega$. Two point particles each of mass M are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity $\omega /2$. Then, the ratio m/M is
Three bricks each of length $L$ and mass $M$ are arranged as shown from the wall. The distance of the centre of mass of the system from the wall is
If the angular momentum of a particle of mass $m$ rotating along a circular path of radius $r$ with uniform speed is $L$, the centripetal force acting on the particle is