Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main20266 April 2026Morning ShiftPhysicsRotational MotionActual

A 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 10 s by applying a constant torque. The torque applied and the number of rotations it made before it comes to rest are _______ and _______ respectively.

Options

  1. A0.128 Nm, 100
  2. B0.0128 Nm, 50
  3. C0.128 Nm, 50
  4. D0.0128 Nm, 100

Correct answer

D. 0.0128 Nm, 100

Step-by-step solution

Initial angular velocity ₀ = 1200 rpm = 1200 2 60 = 40 rad/s Final angular velocity = 0 Time t = 10 s Angular acceleration = - ₀ t = 0 - 40 10 = -4 rad/s ^2 Moment of inertia of the solid sphere I = 2 5 MR^2 = 2 5 5 (0.04)^2 = 0.0032 kg m ^2 Torque = I| | = 0.0032 4 = 0.0128 Nm Angle rotated = ₀ + 2 t = 40 + 0 2 10 = 200 rad Number of rotations N = 2 = 200 2 = 100 Answer: 0.0128 Nm, 100

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 wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first 2 s it rotates through an angle ₁ and in the next 2 s it rotates through an an 2026 Full Rotational Motion list All JEE Main PYQs