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

$\left(A\right)\frac{\mathrm{\pi}}{2}\sqrt{\frac{M}{K}}\phantom{\rule{0ex}{0ex}}\left(B\right)2\mathrm{\pi}\sqrt{\frac{\mathrm{m}}{5\mathrm{K}}}\phantom{\rule{0ex}{0ex}}\left(\mathrm{C}\right)\frac{3\mathrm{\pi}}{2}\sqrt{\frac{\mathrm{M}}{\mathrm{K}}}\phantom{\rule{0ex}{0ex}}\left(\mathrm{D}\right)\mathrm{\pi}\sqrt{\frac{\mathrm{M}}{2\mathrm{K}}}$

what is translatory motion?

A wheel has eight equally spaced spokes and a radius of 30cm. It is mounted on a fixed axle and is spinning at 2.5 rev/s. If we shoot a 20 cm long arrow parallel to this axle and through the wheel without hitting any of the spokes. Assume that the arrow and the spokes are very thin.

(a) What minimum speed the arrow must have?

(b) Does it matter where between the axle and rim of the wheel we aim? If so, what is the best location?

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

^{2}about an axis through it's centre,find gain in angular velocity in 2s.what is the derivation of moment of inertia of solid cone?

_{0}. Two points are located at A and B on rim of ring. Find angular velocity of A w.r.t. B.$\left(1\right)\frac{{v}_{0}}{R}\phantom{\rule{0ex}{0ex}}\left(2\right)\frac{\sqrt{2}{v}_{0}}{R}\phantom{\rule{0ex}{0ex}}\left(3\right)\frac{2{v}_{0}}{R}\phantom{\rule{0ex}{0ex}}\left(4\right)\frac{{v}_{0}}{\sqrt{2}R}$

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?

(1) Constant in magnitude as well as direction

(2) Constant in magnitude only

(3) Constant in direction only

(4) Variable in magnitude as well as direction

pllzzz solve with the help of a diagram

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

i)angular acceleration and

ii)angular velocity after 30 secs

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

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 .

show that moment of inertia of a body about an axis is numerically equal to twice that kinetic energy of rotation of the body rotating at the unit angular velocity about the axis.

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}pls explain m1r1= m2r2...

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???Q.15. An object of mass 10 kg is whirled round a horizontal circle of radius 4 m by a revolving string inclined 30$\xb0$ to vertical. If the uniform speed of the object is 5 m/sec, the tension in the string (approximately) is

1) 720 N

2) 960 N

3) 114 N

4) 125 N

A small ball moves towards right with a velocity V. It collides with the wall and returns back and continues to and fro motion. If the average speed first to and fro motion of the ball is (2/3) V, then the coefficient of revolution of impact is: -

0.5

0.8

0.25

0.75

show that in the absence of any external force, the velocity of the centre of mass remains constant?

Derive a relation between angular momentum, moment of inertia and angular velocity of a rigid body.what is the difference between pure translational motion and translation motion?

(1) l2√(2) l2(3) l(4) l2√

^{2}rotates about its axis at a constant speed of 60rpm under the action of an electric motor of power 31.4 W .if the motor is switched off ,how many roatations will it cover before coming to rest ?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?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))

^{}0.24g of volatile liquid upon vaporisation gives 45ml of vapour at NTP .what will be the vapour density of the substance

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

how to calculate centre of mass of solid hemisphere

Q. The velocities of two steel balls before impact are shown. If after head on impact the velocity of ball B is observed to be 3 m/s to the right, the coefficient of restitution is-

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

A man is standing on the center of a rotating table with arms stretched outwards the table is rotating freely with angular speed of 24 revolution per minute. Now the man withdraws his hand towards his chest thereby reducing moment of inertia 3/5 times his original. Calculate angular speed of man when he withdraws his hand ?

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.

Why are handles of doors fixed maximum away from the hinge end of the door?

Show that for small oscillations the motion of a simple pendulum is simple harmonic. Derive an expression for its time period. Does it depend on the mass of the bob?

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.

^{2}, During a certain 4.0 s interval, it turns through an angle of 120 rad. Assuming that at t = 0, angular speed ω_{0}= 3 rad/s how long, is motion at the start of this 4.0 second interval ?(1) 7 sec. (2) 9 sec. (3) 4 sec. (4) 10 sec.

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.

1.g

2.9g/3

3.2g/3

4.g/2

Q. A uniform solid sphere of mass M= 1 kg and radius R = 50 cm is projected with velocity v

_{0}= 1 m/s and simultaneously given a reverse spin $\omega $_{0}as shown in figure. The horizontal surface is rough. What is initial angular velocity $\omega $_{0}for which rotation and translation stops simultaneously in subsequent motion.(1) 1 rad/s (2) 2 rad/s

(3) 4 rad/s (4) 5 rad/s

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

Q.A wire frame AOPQB, lying in the horizontal plane, is free to rotate about a vertical axis passing through center C of the same circle and perpendicular to plane of AOPQB. The mass M of the frame is uniformly distributed over its whole length. The moment of inertia of the frame about this axis, is(OA = QB = r and CP = r the radius of semicircular part) :-

$\left(A\right)M{r}^{2}\left(\frac{14+3\mathrm{\pi}}{3\mathrm{\pi}+6}\right)\left(B\right)M{r}^{2}\left(\frac{14+3\mathrm{\pi}}{\mathrm{\pi}+2}\right)\phantom{\rule{0ex}{0ex}}\left(C\right)\frac{M{r}^{2}}{2}\left(\frac{\mathrm{\pi}}{2+\mathrm{\pi}}\right)\left(D\right)\frac{1}{2}M{r}^{2}$

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.

31. A particle P is moving along a straight line as shown in the figure. During the motion of the particle from A to B the angular momentum of the particle about O

(1) Increases

(2) Decreases

(3) Remains constant

(4) First increases and then decreases

2) find the torque of force of 2N acting at (0,0) in i direction about point (3,0)

pls i need explanation with diagram

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

total momentum of a system of particles does not depend upon the motion of the particles relative to the centre of mass. But this is not true for total kinetic energy right ? So, does it mean that, when the centre of mass is at rest also, there will be a total kinetic energy of the system ? But how can that be possible ? Pls. clarify...Thnx.

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

written as (Use : g = ${\mathrm{\pi}}^{2}$)

(A) 3$\xb0$ cos $\mathrm{\pi}$t

(B) 3$\xb0$ sin $\mathrm{\pi}$t

(C) 3$\xb0$ sin ($\mathrm{\pi}$t + $\frac{\mathrm{\pi}}{6}$ )

(D) 3$\xb0$ cos ($\mathrm{\pi}$t+$\frac{\mathrm{\pi}}{6}$ )

Plese don't give link.

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 ?

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

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