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

A uniform square plate has a small piece Q of an irregular shape removed and glued to the centre of the plate leaving a hole behind (Figure). The moment of inertia about the z-axis is then ______.

Advertisements
Advertisements

प्रश्न

A uniform square plate has a small piece Q of an irregular shape removed and glued to the centre of the plate leaving a hole behind (Figure). The moment of inertia about the z-axis is then ______.

पर्याय

  • increased

  • decreased

  • the same

  • changed in unpredicted manner

MCQ
रिकाम्या जागा भरा
Advertisements

उत्तर

A uniform square plate has a small piece Q of an irregular shape removed and glued to the centre of the plate leaving a hole behind (Figure). The moment of inertia about the z-axis is then decreased.

Explanation:

In the given diagrams, when the small piece Q is removed and glued to the centre of the plate, the mass comes closer to the z-axis, hence, the moment of inertia decreases.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 7: System of Particles and Rotational Motion - Exercises [पृष्ठ ५१]

APPEARS IN

एनसीईआरटी एक्झांप्लर Physics Exemplar [English] Class 11
पाठ 7 System of Particles and Rotational Motion
Exercises | Q 7.5 | पृष्ठ ५१

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.


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 bullet of mass 10 g and speed 500 m/s is fired into a door and gets embedded exactly at the centre of the door. The door is 1.0 m wide and weighs 12 kg. It is hinged at one end and rotates about a vertical axis practically without friction. Find the angular speed of the door just after the bullet embeds into it.

(Hint: The moment of inertia of the door about the vertical axis at one end is ML2/3.)


Two discs of moments of inertia I1 and I2 about their respective axes (normal to the disc and passing through the centre), and rotating with angular speeds ω1 and ω2 are brought into contact face to face with their axes of rotation coincident. (a) What is the angular speed of the two-disc system? (b) Show that the kinetic energy of the combined system is less than the sum of the initial kinetic energies of the two discs. How do you account for this loss in energy? Take ω1 ≠ ω2.


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 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


Let IA and IB be moments of inertia of a body about two axes A and B respectively. The axis A passes through the centre of mass of the body but B does not. 


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 kid of mass M stands at the edge of a platform of radius R which can be freely rotated about its axis. The moment of inertia of the platform is I. The system is at rest when a friend throws a ball of mass m and the kid catches it. If the velocity of the ball is \[\nu\] horizontally along the tangent to the edge of the platform when it was caught by the kid, find the angular speed of the platform after the event.


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.


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?


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 ______.


Consider a badminton racket with length scales as shown in the figure.

If the mass of the linear and circular portions of the badminton racket is the same (M) and the mass of the threads is negligible, the moment of inertia of the racket about an axis perpendicular to the handle and in the plane of the ring at, `r/2` distance from the ends A of the handle will be ______ Mr2.


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×