मराठी
कर्नाटक बोर्ड पी.यू.सी.पीयूसी विज्ञान इयत्ता ११

A Body Having Its Centre of Mass at the Origin Has Three of Its Particles at (A,0,0), (0,A,0), (0,0,A). the Moments of Inertia of the Body About the X and Y Axes Are 0⋅20 Kg-m2 Each

Advertisements
Advertisements

प्रश्न

A body having its centre of mass at the origin has three of its particles at (a,0,0), (0,a,0), (0,0,a). The moments of inertia of the body about the X and Y axes are 0⋅20 kg-m2 each. The moment of inertia about the Z-axis

पर्याय

  • is 0⋅20 kg-m2

  • is 0⋅40 kg-m2

  • is \[0 \cdot 20\sqrt{2}\]kg-m2

  • cannot be deduced with this information

MCQ
Advertisements

उत्तर

cannot be deduced with this information

 

Ix = m2a2 + m3a2 = 0.20    ......(1)

Iy = m1a2 + m3a2 = 0.20    ......(2)

Iz m1a2 m2a2                ......(3)

We have three equations and four variables. So, Iz cannot be deduced with the given information.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 10: Rotational Mechanics - MCQ [पृष्ठ १९३]

APPEARS IN

एचसी वर्मा Concepts of Physics Volume 1 and 2 [English]
पाठ 10 Rotational Mechanics
MCQ | Q 16 | पृष्ठ १९३

संबंधित प्रश्‍न

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.


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?


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.


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?


A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N? What is the linear acceleration of the rope? Assume that there is no slipping.


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 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 ___________ .


Let I1 an I2 be the moments of inertia of two bodies of identical geometrical shape, the first made of aluminium and the second of iron.


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.


A uniform metre stick of mass 200 g is suspended from the ceiling thorough two vertical strings of equal lengths fixed at the ends. A small object of mass 20 g is placed on the stick at a distance of 70 cm from the left end. Find the tensions in the two strings.


A wheel of mass 15 kg has a moment of inertia of 200 kg-m2 about its own axis, the radius of gyration will be:


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?


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×