हिंदी
कर्नाटक बोर्ड पी.यू.सी.पीयूसी विज्ञान कक्षा ११

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? - Physics

Advertisements
Advertisements

प्रश्न

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

उत्तर

`"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
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

संबंधित प्रश्न

Given the moment of inertia of a disc of mass and radius about any of its diameters to be MR2/4, find its moment of inertia about an axis normal to the disc and passing through a point on its edge


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?


The oxygen molecule has a mass of 5.30 × 10–26 kg and a moment of inertia of 1.94×10–46 kg m2 about an axis through its centre perpendicular to the lines joining the two atoms. Suppose the mean speed of such a molecule in a gas is 500 m/s and that its kinetic energy of rotation is two thirds of its kinetic energy of translation. Find the average angular velocity of the molecule.


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 moment of inertia of a uniform semicircular wire of mass M and radius r about a line perpendicular to the plane of the wire through the centre is ___________ .


A string is wrapped on a wheel of moment of inertia 0⋅20 kg-m2 and radius 10 cm and goes through a light pulley to support a block of mass 2⋅0 kg as shown in the following figure. Find the acceleration of the block.


Suppose the smaller pulley of the previous problem has its radius 5⋅0 cm and moment of inertia 0⋅10 kg-m2. Find the tension in the part of the string joining the pulleys.


A wheel of moment of inertia 0⋅500 kg-m2 and radius 20⋅0 cm is rotating about its axis at an angular speed of 20⋅0 rad/s. It picks up a stationary particle of mass 200 g at its edge. Find the new angular speed of the wheel.


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?


A boy is seated in a revolving chair revolving at an angular speed of 120 revolutions per minute. Two heavy balls form part of the revolving system and the boy can pull the balls closer to himself or may push them apart. If by pulling the balls closer, the boy decreases the moment of inertia of the system from 6 kg-m2 to 2 kg-m2, what will be the new angular speed?


A wheel of moment of inertia 0⋅10 kg-m2 is rotating about a shaft at an angular speed of 160 rev/minute. A second wheel is set into rotation at 300 rev/minute and is coupled to the same shaft so that both the wheels finally rotate with a common angular speed of 200 rev/minute. Find the moment of inertia of the second wheel.


From a circular ring of mass ‘M’ and radius ‘R’ an arc corresponding to a 90° sector is removed. The moment of inertia of the remaining part of the ring about an axis passing  through the centre of the ring and perpendicular to the plane of the ring is ‘K’ times ‘MR2 ’. Then the value of ‘K’ is ______.


Why does a solid sphere have smaller moment of inertia than a hollow cylinder of same mass and radius, about an axis passing through their axes of symmetry?


Moment of inertia (M.I.) of four bodies, having same mass and radius, are reported as :

I1 = M.I. of thin circular ring about its diameter,

I2 = M.I. of circular disc about an axis perpendicular to disc and going through the centre,

I3 = M.I. of solid cylinder about its axis and

I4 = M.I. of solid sphere about its diameter.

Then -


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 cubical block of mass 6 kg and side 16.1 cm is placed on a frictionless horizontal surface. It is hit by a cue at the top to impart impulse in the horizontal direction. The minimum impulse imparted to topple the block must be greater than ______ kg m/s.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×