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how do we derive the moment of inertia of rod, ring, disc, cylinder, sphere and cone?

what is translatory motion?

pl answer Q 20

please derive the centre of mass of a solid cone and a hollow cone.

what is the derivation of moment of inertia of solid cone?

^{2}is spinning with an angular velocity of 15 rad/s. If the wheel is brought to rest by a braking torque in 2.5 seconds , then find the value of torqueFrom a circular disc of radius R and mass 9m, a small disc of radius 3 is removed from the disc,the moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through the center O?

11. A disc of radius a is rigidly attached at its circumference by two rods each of length 3a, two rods are always perpendicular to each other. The combination is suspended vertically the free end of one rod (as shown in figure). It is swinging in the plane of the disc such that the centre of disc have velocity v. If mass of disc and each rod is m.

$\left(\mathrm{A}\right)\mathrm{Kinetic}\mathrm{energy}\mathrm{of}\mathrm{the}\mathrm{disc}\frac{1}{2}{\mathrm{mV}}^{2}+\frac{1}{2}\left(\frac{{\mathrm{ma}}^{2}}{2}\right){\left(\frac{\mathrm{V}}{4\mathrm{a}}\right)}^{2}\phantom{\rule{0ex}{0ex}}\left(\mathrm{B}\right)\mathrm{Kinetic}\mathrm{energy}\mathrm{of}\mathrm{the}\mathrm{rod}2\mathrm{is}\frac{1}{2}{\mathrm{mV}}^{2}+\frac{1}{2}\times \left(\frac{\mathrm{m}{\left(3\mathrm{a}\right)}^{2}}{12}\right)\times {\left(\frac{\mathrm{V}}{4\mathrm{a}}\right)}^{2}\phantom{\rule{0ex}{0ex}}\left(\mathrm{C}\right)\mathrm{Kinetic}\mathrm{energy}\mathrm{of}\mathrm{the}\mathrm{rod}1\mathrm{is}\frac{1}{2}\times \left(\frac{\mathrm{m}{\left(3\mathrm{a}\right)}^{2}}{3}\right)\times {\left(\frac{\mathrm{V}}{4\mathrm{a}}\right)}^{2}\phantom{\rule{0ex}{0ex}}\left(\mathrm{D}\right)\mathrm{Kinetic}\mathrm{energy}\mathrm{of}\mathrm{the}\mathrm{system}\mathrm{of}\left(\mathrm{disc}\mathrm{and}\mathrm{both}\mathrm{rod}\right)\mathrm{is}\phantom{\rule{0ex}{0ex}}\frac{1}{2}\left[\left(\frac{\mathrm{m}{\left(3\mathrm{a}\right)}^{2}}{3}\right)+\left(\frac{{\mathrm{ma}}^{2}}{2}+\mathrm{m}{\left(4\mathrm{a}\right)}^{2}\right)+\left(\frac{\mathrm{m}{\left(3\mathrm{a}\right)}^{2}}{12}+\mathrm{m}\frac{89}{4}{\mathrm{a}}^{2}\right)\right]{\left(\frac{\mathrm{V}}{4\mathrm{a}}\right)}^{2}\phantom{\rule{0ex}{0ex}}$

difference between centre of gravity and centre of mass

of intertia of the disc about its centre is

50) 2 spherical bodies of mass M and 5M are of radii R and 2R respectively are released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller bady just before collision is

a) 1.5R b)2.5R c)4.5R d)7.5R

Q. Find the torque of a force 7i+3j-5k about the origin. The force acts as on a partical whose position vector is i-j+k .

what happens to the center of mass of a firecracker when it explodes in air?

A neutron travelling with a velocity v and kinetic energy E collides elastically head on with the nucleus of an atom of mass number A at rest. The fraction of total energy retained by the neutron is

^{2}^{2}^{2}^{2}four point masses are placed at the corners of a square of side 2m . find the centre of mass of the system wrt to the centre of square. the masses of objects placed are 1kg,2kg.3kg and 4kg.A particle performs uniform circular motion with the angular momentum L. If the frequency of the particle motion is double and its kinetic energy is half...what happens to its angular momentum???there is a uniform bar or mass m and length l hinged at the centre, so that it can turn in a vertical plane about a horizontal axis. Two point like masses m and 2m are rigidly attached to the ends and the arrangement is released from rest. Find (i) the initial angular acceleration of the bar (ii) the initial acceleration of mass 2m (iii) the initial reaction at hinge (iv) the angular speed aquired by the bar as it becomes vertical.

a ball moving with a speed 9m/s strikes an identical ball at rest , such that after the collisoins, the direction of each ball makes an angle of 30 degree with original line of motion.. find the speed of two balls after collisins

the earth to a depth to

12

th radius of the earth,

then the weight of the body at that point is

(A) 40 kg-wt (B) 20 kg-wt

(C) 30 kg-wt (D) zero

Derive a relation between angular momentum, moment of inertia and angular velocity of a rigid body.(1) l2√(2) l2(3) l(4) l2√

1.Force in the string

2.Magnitude of hinge force

The moment of inertia of two rotating bodies are I

_{A}and I_{B}(I_{A}I_{B}) and their angular momenta are equal. Which one has greater kinetic energy?0.24g of volatile liquid upon vaporisation gives 45ml of vapour at NTP .what will be the vapour density of the substance

1) Find the tension in the pendulum at the extreme position if amplitude is q .

2) A sphere of mass 0.2 kg is attached to an inextensible string of length of 0.5 m whose upper end is fixed to the celling . the sphere is made to describe a horizontal circle of radius 0.3m . the speed of the sphere will be ?

3) Two wires ac and bc are tied at c of small sphere of mass 5kg , which revolves at a constant speed v in the horizontal circle of radius 1.6 m . the minimum value of v is ?

4) A man is supported on a frictionless horizontal surface . it is attached to a spring and rotates about a fixed centre at an angular velocity 20. The tension in the string is f, of the length of string and angular velocity are doubled , the tension in string is now?

5) A car of mass 1000kg moves on a circular track of radius 20m . if the coefficient of friction is 0.64 , then the maximum velocity with which the car can moves is?

6) Moment of inertia of a thin rod of mass m and length l about an axis passing through its centre is ml/m its moment of inertia about a parallel axis at a distance of l/4 from this axis is given by ?

7) A solid cylinder of mass 20 kg has length 1m and radius 0.2m . then its moment of inertia in kg m2 about its geometrical axis is?

a) T = mg b) T = $\frac{mg}{2}$ c) T = $\frac{mg}{4}$ d) T = zero

how to calculate centre of mass of solid hemisphere

(i,j are unit vectors in vertical plane)

state parallelogram law of vector addition. derive analytically expression for magnitude and direction of resultant vector

59) A tube of length L is filled completely woth an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of it's ends with a uniform angular velocity w. The force exerted by the liquid at the other end is (answer in terms og M, L and w(angular velocity))

^{}24) The moment of inertia of a disc about an axis tangential and parallel to it's surface be I, then what will be the moment of Inertia about the axis tangential but perpendicular to the surface.

25) A solid sphere ball rolls on an inclined plane without slipping. The ratio of the rotational energy and rolling energy.

^{2}. then the rate of change of centripetal acceleration increasing at the instant will be:a) 200m/s

^{3}b) 600 m/s3 c) 100 m/s^{2}d) 300 m/s3aand massm, a square portionDEFGof side $\frac{a}{2}$ is removed. Then, the moment of inertia of remaining portion about the axisABis(a) $\frac{7m{a}^{2}}{16}$ (b) $\frac{3m{a}^{2}}{16}$ (c) $\frac{3m{a}^{2}}{4}$ (d) $\frac{9m{a}^{2}}{16}$

ans; 5.4m/s

Four spheres of diameter 2a and mass M each are placed with their centres at four corners of a square of side b. Calculate the moment of inertia of the system about one side of the square taken as its axis ?

a) tan

^{-1}(1/4)b) tan

^{-1}(1/3)c) tan

^{-1}(1/2)d( cot

^{-1}(1/4)system about an axis passing through, the centre of mass and normal to its plane.

pl ans Q21

pls explain m1r1= m2r2...

a. 1:3

b. 1:2

c. 2:7

d. 2:5

***I want answer with full solution as soon as possible***

(a) through A

(b) through the mid- point of AB.

Derive an expression for work done by torque and its power.

I you have eight one kilogram blocks,how many different combination are possible so that the centre of mass comes to the center of sq ABCD. All blocks can be kept at corners of sqABCD only.

(a) the angular acceleration of the plate

(b) the acceleration of its mass center.

Answer is: (a) 24g/17c

Two discs of moments of inertia

I_{1}andI_{2}about their respective axes (normal to the disc and passing through the centre), and rotating with angular speeds ω_{1}and ω_{2}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 ω_{1}≠ ω_{2}.Why are handles of doors fixed maximum away from the hinge end of the door?

URGENT ! a child is standing at one end of a long trolley moving with a speed v on a smooth horizontal track . if the child starts running towards the other end of the trolley with a speed u , then the centre of mass of the system ( trolley + child) will move with a speed ???

find the centre of mass of three particles at the vertices of an equilateral triangle. the masses of the particles are 100g, 150g and 200g respectively. each side of the triangle is 0.5cm long. if two vertices of the triangle are (0,0) and (0.5,0). what will be the third vertex.

9.8 m/ ${s}^{2}$)

$a.\frac{2\mathrm{\pi}}{7}sec\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}b.\frac{\mathrm{\pi}}{7}sec\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}c.\frac{2\mathrm{\pi}}{5}sec\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}d.noneofthese$

A bullet of mass m moving with velocity v strikes a suspended wooden block of mass M at rest. If the collision is inelastic block rises to a height h, What will the initial velocity of the bullet ?

find:

1) the angular velocity of system after the collision

2) the velocities of A and B immediately after the collision

3) the velocity of the centre of the rod when the rod rotates through 90 degree after the collision

Define Angular velocity and Angular acceleration?

my question is not related to topic but i wana answer to my question urgenty..

Q:DURING LIGHTINING NAD THUNDER SUM SOLID MATERIAL FALLS.. WAT IZ DAT SOLID MATERIAL AND HOW IZ DAT FORMED IN AIR???????

PLZZZZZZ ANSWER IT

Problem: A circular plate of uniform thickness has a diameter of 56 cm. A circular portion of diameter 42cm is removed from one edge of the plate. Find the position of the center of mass of the remaining portion.

Please reply by 13th morning, since exam on 14th morning.

What is the derivation for v=rw?

Although my profile is complete yet it is showing only 85% complete.Why?

If angular momentum is conserved in a system whose moment of inertia is decreased, Will its rotational kinetic energy be also conserved? Explain.

From a square sheet of uniform density, one of the four portions within its diagonals is removed .. Find the of centre of mass of a remaining portion if the side of the square is a. The portion removed is right one

An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 m/s and the second part of mass 2 kg moves with 8 m/s speed. If the third part flies off with 4 m/s speed, then its mass is??

On what factors does the radius of gyration depend?

three particles each of mass m are placed at three corner of an equilateral triangle of length l. find the position of center of mass in terms of coordinates

A wheel of 16 kg mass and 50 cm radius is pulled

by a force of 8 N applied on the string wound onthe wheel suspended at S. Angular speed of thewheel after 10 sQ. A sphere of mass m rolls without slipping on an inclined plane of inclination theta. Find the linear acceleration of the sphere and the force of friction acting on it. What should be the minimum coefficient of static friction to support pure rolling ?