Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main2013PhysicsRotational MotionActual

A ring of mass M and radius R is rotating about its axis with angular velocity . Two identical bodies each of mass m are now gently attached at the two ends of a diameter of the ring. Because of this, the kinetic energy loss will be :

Options

  1. Am(M+2 m) M ^2 R^2
  2. BM m (M+m) ^2 R^2
  3. CM m (M+2 m) ^2 R^2
  4. D(M+m) M (M+2 m) ^2 R^2

Correct answer

C. M m (M+2 m) ^2 R^2

Step-by-step solution

Kinetic energy _ (rotational) K _ R = 1 2 I ^2 Kinetic energy _ (translational) K _ T = 1 2 Mv ^2 aligned & ( v = R ) & M.I. _ (initial) I _ ring = MR ^2 ; _ initial = & M.I. _ (new) I ^ _ (system) = MR ^2+2 mR ^2 & _ ( system) ^ = M M+2 m & aligned Solving we get loss in K.E. = Mm ( M +2 ~m ) ^2 R ^2

Practice Rotational Motion on Quantrex Academy →

More from Rotational Motion

Consider a large disk of radius R and two smaller disks, each of radius r = R/50 , lying on its circumference, as shown in the figure. The smaller disks are initially in contact wi 2026A solid cylinder of radius R rolls without slipping with a center of mass speed v₀ = gR 3 on a horizontal surface with a vertical edge, as shown in the figure. Here, g is the accel 2026List-I shows four planar structures made of uniform solid rods each of mass m and length l . In the List-II the possible moment of inertia of these structures about an axis OCO' , 2026Passage: A uniform circular disk of radius 0.2 m and mass 1 kg is pivoted at its top point C such that it can rotate freely around C in the XY plane, as shown in the figure. Initia 2026Passage: A uniform circular disk of radius 0.2 m and mass 1 kg is pivoted at its top point C such that it can rotate freely around C in the XY plane, as shown in the figure. Initia 2026A solid cylinder having radius R and length L is slipping on a rough horizontal plane. At time t=0 the cylinder has a translational velocity v₀=49 m/s, perpendicular to its axis an 2026A solid sphere ( A ) of mass 5m and a spherical shell ( B ) of mass m , both having same radius, are placed on a rough surface. When a force of same magnitude is applied tangential 2026A solid sphere of radius 4 cm and mass 5 kg is rotating (rotation axis is passing through the centre of the sphere) with an angular velocity of 1200 rpm. It is brought to rest in 1 2026 Full Rotational Motion list All JEE Main PYQs