Moment of Inertia of a Rod

Q.

Two rings have their moment of inertia in the ratio 2:1 and their diameters are in the ratio 2:1. The ratio of their masses will be:

1. 1:1

2. 1:2

3. 2:1

4. 1:4

Q. A particle of mass 1Kg is kept at ( 1m, 1m, 1m). The moment of inertia of this particle about z axis would be?

Q. There are four point masses M each on the corners of a square of side length L.what is the moment of inertia of the system about one of its diagonal

Q. Two point masses m and 2m are joined by light rod of length d. The moment of inertia of the system about an axis passing through its Centre of mass and making an angle 30° with the light rod will be

Q. 38. Consider a uniform rod of mass m and length 2l wth two particles of mass m each at its ends. Let AB be line perpendicular to the length of the rod and passing through the centre.find moment of inertia of the system about AB.

Q. how to find direction in angular momentum

Q.

what is the meaning of radius of gyration?

Q. Four particles each of mass 2 kg are kept at the four corners of a square of edge length 2 m. The moment of inertia of the system about an axis which is perpendicular to the plane of the square and passing through centre of square is A 4 kg m2 B 8 kg m2 C 16 kg m2 D 8√2 kg m2

Q. show that in an isolated system linear momentum is conserve

Q. Three masses m1, m2 and m3 are located at the vertices of an equilateral triangle of side a.What is the moment of inertia of the system about the axis along the medium passing through m1?

Q. 98.A thin disc of mass 9M and radius R from which a disc of radius is cut.Moment of inertia of the disc about an axis passing through O and perpendicular to the plane of disc is

Q. four masses each of 2 kg are placed on a horizontal circular disc which can be rotated about a vertical Axis passing through its centre and all the masses be equidistance from the axis and at a distance of 10 cm from it the moment of inertia of the whole system is:(assume disc is of negligible mass)

Q. When the axis of rotation passes through itscentre of gravity, then the moment of inertia of arigid body is(1) Reduced to its minimum value(2) Zero(3) Increased to its maximum value(4) Infinity

Q. Three identical rods, each of mass $m$ and length $l$, form an equilateral triangle. Moment of inertia about one of the sides is

1. $\frac{m{l}^2}{4}$
2. $m{l}^2$
3. $\frac{3m{l}^2}{4}$
4. $\frac{m{l}^2}{2}$

Q. .4) A small hole is made in a disc of mass M and radius R at a distance R/4 from centre. The disc is supported at the peg through this hole. The moment of inertia of disc about horizontal peg is

Q.

Two masses are in the ratio 1:5. What is ratio of their inertia?

1. 25 : 1

2. 1 : 25

3. 1 : 5

4. 5 : 1

Q. 23.A solid cylinder has mass M, length L and radius R. The moment of inertia of this cylinder about diameter is

Q. Three point masses, each of mass 10 kg are2.olaced at the vertices of an equilateral triangle ofside 2 m (one mass on one vertex). The momentof inertia of the system about any side is(1) 10 kg m2(2) 30 kg m210x43(3) 20 kg m24 kg m2

Q. a disc is made to rotate about a horizontal fixed axis with the help of a body of mass 5 kg attached to a string wound around the dsc the radius of the disc . the radius of the disc is 10 cm . the body falls vertically trough 10 m in 10 sec starting from rest . momment of inertia of disc

Q. Two small particles each of mass m are attached atthe two ends of a semicircular ring of same mass asshown. R is radius of ring and O is the centre of thering. Moment of inertia about an axis through Onormal to its plane is

Q. if a constant couple of 500 Nm turns a wheel of moment of inertia 100 kg m square about an axis through its centre the angular velocity gained is?

Q. A thin rod has a length of $5\text{m}$. What is the ratio of the $\text{MI}$ of the rod about an axis perpendicular and passing through it's centre, to $\text{MI}$ of the rod about an axis perpendicular and passing through one of the edges of the rod?

1. $\frac{1}{4}$
2. $4$
3. $2$
4. $\frac{1}{2}$

Q. 37. Four rings each of mass M and radius R are arranged as shown in the figure. The moment of inertia of the system about the axis yy is

Q. 105.calculate the moment of inertia of a ring about a tangent to the circle of the ring normal to its plane

Q. A thin rod of length $4l$, mass $4m$ is bent at the points shown in the figure. What is the moment of inertia of the rod about the axis passing point $\text{O}$ and perpendicular to the plane of the paper?

1. $\frac{M{l}^2}{3}$
2. $\frac{10M{l}^2}{3}$
3. $\frac{M{l}^2}{12}$
4. $\frac{M{l}^2}{24}$

Q. a round disc of moment of inertia I1 about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia I2 rotating with an angular velocity w about same axis the final angular velocity of the combination of disc

Q. A metal rod of mass m and length L is pivoted at A.A thin disc of mass 2m and radius R(< L) is attachedat C such that the disc is free to rotate about itscentre. The moment of inertia of the system about AIS

Q. Four holes of radius R are cut from a thin square plate of side 4R and mass M .Determine the moment of inertia of remaining portion about Z axi

Q. let there be two non inertial frames with same acceleration a. are the frames inertial with respect to each other

Q. a uniform disc of radius R lies in x y plane with its centre at origin .its moment of inertia about z axis is equal to its moment of inertia about line y =x+c the value of c is