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Syllabus

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

Prove that Kinetic Energy of rotation E= 1/2 IW

^{2 }WHERE SYMBOLS HAVE THEIR USUAL MEANINGwhat is translatory motion?

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.

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

pls explain m1r1= m2r2...

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?

if a disc slides from top to bottom of an inclined plane ,it takes time t1.If it rolls, it takes time t2 .Now t

_{2}^{2}/t_{1}^{2i}s________difference between centre of gravity and centre of mass

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.

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

^{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/s3Q. 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.pllzzz solve with the help of a diagram

(1) l2√(2) l2(3) l(4) l2√

(A) $\mathrm{M}\left(\frac{{\mathrm{R}}^{2}+{\mathrm{r}}^{2}}{2}\right)+\frac{\mathrm{M}{\mathcal{l}}^{2}}{12}$

(B) $\mathrm{M}\left(\frac{{\mathrm{R}}^{2}+{\mathrm{r}}^{2}}{2}\right)+\frac{\mathrm{M}{\mathcal{l}}^{2}}{3}$

(C) $\mathrm{M}\left(\frac{{\mathcal{l}}^{2}+3{\mathrm{R}}^{2}-3{\mathrm{r}}^{2}}{12}\right)$

(D) $\mathrm{M}\left(\frac{{\mathrm{R}}^{2}+{\mathrm{r}}^{2}}{4}\right)+\frac{\mathrm{M}{\mathcal{l}}^{2}}{12}$

why moment of mass about centre is zero?

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?a) downwards at end A

b) downwards at mid point of AB

c) downwards at at point C such that AC=1m

d) downwards at at point D such that BD=1m

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

Why is the handle of a screw-driver is made wide?

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

a.√19.6 m/sec

b.√29.4 m/sec

c. 4.9 m/sec

d. 9.8 m/sec

***Inwant answer with full solution as soon as possible***

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.

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

ans; 5.4m/s

Please provide the answer to the above given question urgently.

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.

acceleration of the bar immediately after it has been released from rest, knowing that the normal forces exerted on the disks are sufficient to prevent any slipping and assuming that;

(a) m = 5 kg and m' = 2kg.

(b) the mass of m' of the disks is negligible.

(c) the mass of m of the bar is negligible.

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.

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

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 ?

Q7. Two identical disc having radius R are rotating in opposite sense are joined with light rod having frictionless groove A and B and placed on rough horizontal surface as shown in figure. Initially translation velocity of each disc is zero. Then :-

(A) Final velocity of B is $\frac{{\mathrm{R\omega}}_{0}}{6}$

(B) Rod's length will increase initially due to stress

(C) Finally rod has tensile stress

(D) Mechanical energy will decrease

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

_{0}is The instantaneous speed of point p as shown is (1) v_{0}(2) v_{0}(3) v_{0 }(4) v_{0}/^{2}+5t+16 and where y=5t where x,y are in metre and t is in second.the acceleration of the particle is?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 analogus of mass in rotational motion? Write the unit of that physical quantity.

What is the derivation for v=rw?

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 ?

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

Q.9. A solid cylinder rolls without slipping along a horizontal plane with velocity 66 m/s and reaches a plane inclined at 60$\xb0$ with the horizontal. If there is sufficient friction to prevent slipping then the body starts rolling up the inclined plane with the velocity v. Find the value of v (in m/s).

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

What is the radius of gyration of a disc of radius 20 cm, rotating about an axis passing through its center and normal to its plane?

1. R

2.3R/2

3.2R

4.5R/2