English
Karnataka Board PUCPUC Science Class 11

Show that the Child’S New Kinetic Energy of Rotation is More than the Initial Kinetic Energy of Rotation. How Do You Account for this Increase in Kinetic Energy?

Advertisements
Advertisements

Question

Show that the child’s new kinetic energy of rotation is more than the initial kinetic energy of rotation. How do you account for this increase in kinetic energy?

Advertisements

Solution

`"Final Kinetic Energy of rotation"/"Initial Kinetic Energy of rotation"  = (1/2 I_2omega_2^2)/(1/2I_1omega_1^2) = (1/2 I_2(2piv_2)^2)/(1/2I_1(2piv_1)^2) = (I_2v_2^2)/(I_1v_1^2) = (2/5I_1xx(100)^2)/(2/5I_1xx(40)^2) = 2.5`

Clearly, final (K.E) becomes more because the child used his internal energy when he folds his hands to increase the kinetic energy

shaalaa.com
  Is there an error in this question or solution?

RELATED QUESTIONS

Find the moment of inertia of a sphere about a tangent to the sphere, given the moment of inertia of the sphere about any of its diameters to be 2MR2/5, where is the mass of the sphere and is the radius of the sphere.


Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. Which of the two will acquire a greater angular speed after a given time?


Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. Which of the two will acquire a greater angular speed after a given time?


A child stands at the centre of a turntable with his two arms outstretched. The turntable is set rotating with an angular speed of 40 rev/min. How much is the angular speed of the child if he folds his hands back and thereby reduces his moment of inertia to 2/5 times the initial value? Assume that the turntable rotates without friction.


A hoop of radius 2 m weighs 100 kg. It rolls along a horizontal floor so that its centre of mass has a speed of 20 cm/s. How much work has to be done to stop it?


A solid cylinder rolls up an inclined plane of angle of inclination 30°. At the bottom of the inclined plane, the centre of mass of the cylinder has a speed of 5 m/s.

(a) How far will the cylinder go up the plane?

(b) How long will it take to return to the bottom?


The descending pulley shown in the following figure has a radius 20 cm and moment of inertia 0⋅20 kg-m2. The fixed pulley is light and the horizontal plane frictionless. Find the acceleration of the block if its mass is 1⋅0 kg.


A diver having a moment of inertia of 6⋅0 kg-m2 about an axis thorough its centre of mass rotates at an angular speed of 2 rad/s about this axis. If he folds his hands and feet to decrease the moment of inertia to 5⋅0 kg-m2, what will be the new angular speed?


Two blocks of masses 400 g and 200 g are connected through a light string going over a pulley which is free to rotate about its axis. The pulley has a moment of inertia \[1 \cdot 6 \times  {10}^{- 4}   kg -  m^2\] and a radius 2⋅0 cm, Find (a) the kinetic energy of the system as the 400 g block falls through 50 cm, (b) the speed of the blocks at this instant.


The pulley shown in the following figure has a radius of 20 cm and moment of inertia 0⋅2 kg-m2. The string going over it is attached at one end to a vertical spring of spring constant 50 N/m fixed from below, and supports a 1 kg mass at the other end. The system is released from rest with the spring at its natural length. Find the speed of the block when it has descended through 10 cm. Take g = 10 m/s2.


Four bodies of masses 2 kg, 3 kg, 4 kg and 5 kg are placed at points A, B, C, and D respectively of a square ABCD of side 1 metre. The radius of gyration of the system about an axis passing through A and perpendicular to plane is


With reference to figure of a cube of edge a and mass m, state whether the following are true or false. (O is the centre of the cube.)

  1. The moment of inertia of cube about z-axis is Iz = Ix + Iy
  2. The moment of inertia of cube about z ′ is I'z = `I_z + (ma^2)/2`
  3. The moment of inertia of cube about z″ is = `I_z + (ma^2)/2`
  4. Ix = Iy

Four equal masses, m each are placed at the corners of a square of length (l) as shown in the figure. The moment of inertia of the system about an axis passing through A and parallel to DB would be ______.


The figure shows a small wheel fixed coaxially on a bigger one of double the radius. The system rotates about the common axis. The strings supporting A and B do not slip on the wheels. If x and y be the distances travelled by A and B in the same time interval, then ______.


A thin circular plate of mass M and radius R has its density varying as ρ(r) = ρ0r with ρ0 as constant and r is the distance from its center. The moment of Inertia of the circular plate about an axis perpendicular to the plate and passing through its edge is I = a MR2. The value of the coefficient a is ______.


The moment of inertia of a thin rod about an axis passing through its mid point and perpendicular to the rod is 2400 g cm2. The length of the 400 g rod is nearly ______.


A sphere of radius R is cut from a larger solid sphere of radius 2R as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the Y-axis is:


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×