Class XI Physics System of Particles and Rotational Motion Quiz 10

A disc of mass 2 kg and radius 0.2 m is rotating with angular velocity 30 rads^-1. What is angular velocity(in rad s^-1),  if a mass of 0.25 kg is put on periphery of the disc?

A solid sphere of mass m rolls down an inclined plane without slipping, starting from rest at the top of an inclined plane. The linear speed of the sphere at the bottom of the inclined plane is v. The kinetic energy of the sphere at the bottom is

Two masses m₁ and m₂ are connected by a massless spring of spring constant k and upstretched length l. The masses are placed on a frictionless straight channel – which we consider our x-axis. They are initially at rest at x = 0 and x = l, respectively. At t = 0, a velocity of v₀ is suddenly imparted to the first particle. At a later time t, the center of mass of the two masses is at

A sphere is rolling without slipping on a rough movable wedge as shown in the figure. If a₀ is the acceleration of wedge, a is the acceleration of centre of mass of sphere w.r.t. wedge, N is the normal reaction on the sphere and f_r is the frictional force on the sphere, then select the correct equation (neglect the friction between ground and wedge)