Rotational Motion - Physics PYQ | AP EAPCET

A girl of mass M stands on the rim of a frictionless merry-go-round of radius R and rotational inertia I, that is not moving. She throws a rock of mass m horizontally in a direction that is tangent to the outer edge of the merry-go-round. The speed of the rock, relative to the ground is v. Afterwards, the linear speed of the girl is

A sphere of mass m is attached to a spring of spring constant k and is held in unstretched position over an inclined plane as shown in the figure. After letting the sphere go, find the maximum length by which the spring extends, given the sphere only rolls.

Which of the following type of wheels of same mass and radius will have largest moment of inertia?

As solid sphere of mass \(M\) and radius \(R\) spins about an axis passing through its centre making \(600 \mathrm{~rpm}\). Its kinetic energy of rotation is

Two fly wheels \(A\) and \(B\) are mounted side by side with frictionless bearings on a common shaft. Their moments of inertia about the shaft are \(5.0 \mathrm{~kg}-\mathrm{m}^2\) and \(20.0 \mathrm{~kg}-\mathrm{m}^2\), respectively. Wheel \(A\) is made to rotate at \(10 \mathrm{~rev}\) per second. Wheel \(B\), initially stationary, is now coupled to \(A\) with the help of a clutch. The rotation speed of the wheels will become

A sphere and a hollow cylinder without slipping, roll down two separate inclined planes A and B, respectively. They cover same distance in a given duration. If the angle of inclination of plane A is 30\(^\circ\), then the angle of inclination of plane B must be (approximately)

Four spheres each of diameter \(2 a\) and mass \(m\) are placed in a way that their centers lie on the four corners of a square of side \(b\). Moment of inertia of the system about an axis along one of the sides of the square is

If an energy of 684 J is needed to increase the speed of a flywheel from 180 rpm to 360 rpm, then find its moment of inertia.

A solid sphere of radius \(R\) has its outer half removed, so that its radius becomes \((R / 2)\). Then its moment of inertia about the diameter is

Consider a disc of radius \(R\) and mass \(M\). A hole of radius \(\frac{R}{3}\) is created in the disc, such that the centre of the hole is \(\frac{R}{3}\) away from centre of the disc. The moment of inertia of the system along the axis perpendicular to the disc passing through the centre of the disc is

A solid cylinder of radius \(R\) is at rest at a height \(h\) on an inclined plane. If it rolls down then its velocity on reaching the ground is