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

what is translatory motion?

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?

From 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?

difference between centre of gravity and centre of mass

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 .

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???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

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

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

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

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.

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 ?

system about an axis passing through, the centre of mass and normal to its plane.

a. 1:3

b. 1:2

c. 2:7

d. 2:5

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

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

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}.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.

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

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?

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

Q. 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 ?