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Syllabus

what is physical significance of moment of inertia?

state and explain theorem of perpendicular and parellel axis what ia moment of inertia about circular disc

A force acts on a 3g particle in such a way that the position of the particle as a function of time is given by x=3t-4t

^{2}+t^{3}where x is in meters and t is in seconds. The work done during the first 4 sec.

_{m’.}[b]Also show that the spring force is conservative force.[c]Derive the expression to find the maximum velocity of the spring when it crosses the mean position.Show that a Gravitational Force is a Conservative Force .

1)a ball is thrown vertically upwards . Draw velocity time graph of this motion?

2)define angle of friction?

3)the speed of a projectile reduces to 50% on reaching maximum height. what is the horizontal range?

4)distinguish b/w elastic & nonelastic collision .give 1 example for each

The relation between the displacement x and the time t for a body of mass 2kg moving under the action of force is given by x=t

^{3}/3 , where x is in metre and t in second , calculate the work done by body in first 2 seconds.^{-1}. A second body of mass 10kg moves along the Y-axis with the velocity of (root3)ms^{-1}. they collide at the origin and stick together. calculate(a).The final velocity of the combined mass after collision

(b).The amount of heat liberated in the collision.

A running man has half the kinetic energy that a boy half his mass has. The man speeds up by 1.0m/s and then has the same energy as the boy. What were the orignal speed of the man and the boy?

x^{2}y^{2}i+x^{2}y^{2}j(N) acts on a particle which moves in the XY plane.(a) Determine F is conservative or not and

(b) Find the work done by F as it moves the particle from A to C (fig.) along each of the paths ABC, ADC, and AC.

a uniform chain of lenght L and mass M is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. if g is acceleration due to gravity,calculate work required to pull the hanging part on th table

^{-1}. Then^{-1}^{-2}define escape velocity .derive expression for it

prove work energy theorem for a variable force

give 4 examples of positive, negative and zero work done with diagram

a force F=-K(yi+xj), where K is a positive constant,acts on a particle moving in a x-y plane.. starting from the origin yhe particle is taken alon positive x axisto a point (a,0) and then parallel to y axis to a point (a,a.) calculate the total work done by force on the particle.

what is the angle between (icap +jcap) and (icap - jcap)?

a running man has half the k.e of that of a boy of half his mass.the man speeds up by 1m/s and then has the same k..e as that of boy. find original speeds of man and boy

Does the center of mass of a body always lie inside the body?

8. Using Kirchhoff's rules in the given circuit,determine

(i) the voltage drop across the unknown resistor R and

(ii) the current I

_{2}in the arm EF.â€‹a) 3 m/s

b) 4 m/s

c) 6 m/s

d) 8 m/s

compression of the spring.

A shell is fired from a cannon with a velocity v m/s at an angle theta with the horizontal direction.At the highest point of this path , it explodes into two pieces of equal mass. One of the pieces retraces its path to the cannon.The speed in m/s of other piece immediately after the explosion will be ?

show that total energy is conserved at any instant of time (mathematically) in the following cases:

freely falling body;

spring;

bouncing of a ball;

increase in potential energy is

(1) $mg\frac{l}{2}\left(1-\mathrm{cos}\theta \right)$

(2) $mg\frac{l}{2}\left(1+\mathrm{cos}\theta \right)$

(3) $mg\frac{l}{2}\left(1-\mathrm{sin}\theta \right)$

(4) $mg\frac{l}{2}\left(1+\mathrm{sin}\theta \right)$

A man pulls a bucket of water from a well of depth H. if the mass of uniform rope and bucket full of water are m and M respectively. The value of work done by man is

A.(M+m/2).g.h

B.(M+m)gh

C.(m+M)/2.G.H

D. none

A ball is dropped vertically from rest at a height of 12m. After striiking the ground , it bounces back to a height of 9m. What fraction of kinetic energy does it lose on striking the ground?

A bob of mass m is suspended by a light string of length L.It is imparted a horizontal velocity v

_{0}at the lowest point A such that it completes a semi- circular trajectory in the vertical plane with the string becoming slack only on reaching the topmost point,C.Obtain an expression fori) v

_{0}ii)the speeds at point B and C

NUMERICAL.

A vehicle of mass 30 quintals moving with a speed of 18km/hr collides with another vehicle of mass 90 quintals moving with a speed of 14.4 km/hr. What will be the velocity of each after the collision if they are in opposite directions?

A long spring is stretched by 2 cm when P.E. is V. If the spring is stretched by 10 cm, what is the value of P.E.?

A train weighing 100 metric ton is running on a level track with a uniform speed of 72 km/h.If the frictional resistance amounts 0.5 kg per metric ton,find the power of the engine.choose one:

$\overline{)}15\left[5\hat{i}+6\hat{j}+5\hat{k}\right]\phantom{\rule{0ex}{0ex}}\overline{)}15\left[5\hat{i}+6\hat{j}-5\hat{k}\right]\phantom{\rule{0ex}{0ex}}\overline{)}150\left[5\hat{i}-6\hat{j}+5\hat{k}\right]\phantom{\rule{0ex}{0ex}}\overline{)}150\left[5\hat{i}+6\hat{j}+5\hat{k}\right]$

An engine pumps water through a hose pipe. water passes through the pipe & leaves it with a velocity of 2 m/s. the mass per unit length of water in the pipe is 100 kg/m. what is the power of the engine?

_{A}& m_{B }respectively, then:-a) 2m

_{A}=m_{B}b) 3m

_{A}=m_{B}c) 4m

_{A}=m_{B}d) (3)

^{1/}^{2}m_{A}=m_{B}HOW DOES THE KINETIC ENERGY OF A BODY CHANGE IF ITS MOMENTUM IS DOUBLED ?An elastic spring of spring constant k is compressed by an amount x . show that its potential energy is 1/2k x2 .

plz explain me integration and differentiation with basics and examples and formulas.....plzzzz badly needed.....help as soon as posssible.....reply awiated!!!!!!

a bullet moving at a speed of 400m/s just pierces a wooden block 4cm thick.what speed will be required to just pierce a block 9cm thick?

1. An object is attached to a vertical spring and slowly lowered to its equilibrium position. This stretches the spring by a distance d.if the same object is attached to the same vertical spring but permitted to fall freely, through what distance does it stretches the spring.

2.A block of 2 kg is dropped from a height of 40 cm on a spring of force constant 1960 N/m what will be the maximum distance x to which the spring is compressed.

1/19thof its mass? [ans- 99.8%]a body of mass M at rest is struck by a moving body of mass m. prove that the fraction of initial K.E of mass transferred to the struck body is 4Mm/(m+M)^2

A block of mass m is attached to two unstretched springs of spring constants k1 and k2 as shown in figure.The block is displaced towards right through x and is released. Find the speed of the block as it passed through the mean position.

A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time

tis proportional to(i) (ii)

t(iii) (iv)_{}prove that spring force is a conservative force,The blades of a windmill sweep out a circle of area

A. (a) If the wind flows at a velocityvperpendicular to the circle, what is the mass of the air passing through it in timet?(b) What is the kinetic energy of the air? (c) Assume that the windmill converts 25% of the wind’s energy into electrical energy, and thatA= 30 m^{2},v= 36 km/h and the density of air is 1.2 kg m^{–3}. What is the electrical power produced?if kinetic energy of the body is increase by 300 percent then by what percent will its linear momentum increase

_{1=}m_{2, }u_{2=}0)two vectors of equal magnitude have a resultant equal to either of them, then the angle between them will be equal to...?

A particle is acted upon by a constant force f1 =2i -3 j+ 4k and F2 =-i+2j-3k is displaced from the point A(2,1,0) to the point B (-3,-4.2) find the total work done by these forceA ball falls from a height such that it strikes the floor of lift at 10 m/s.If lift is moving in the upward direction with a velocity 1 m/s, then velocity with which the ball rebounds after elastic collision will be?

a particle of mass m moving with speed V collides perfectly inelastically with another particle of mass 2m at rest. fractional loss of kinetic energy of the system in the collision is

An elevator can carry a maximum load of 1800kg, is moving up with a constant speed of 2m/s. The frictional force opposing the motion is 4000N. Determine the minimum power delivered by the motor to the elevator in watts. (take g=9.8m/s

^{2}^{-27}kg is moving with a speed of 7 x 10^{5}ms^{-1}. Calculate(i) The kinetic energy and (ii) the average force it will expert in entering a body to a depth of 0.01 cm.

Q21. A bullet of mass 20 g strikes a target with a velocity of 150 ms-1 and brought to rest after piercing 10 cm into it. Calculate the average force of resistance offered by the target.

A chain of mass M is placed on a smooth table with 1/n of its length L hanging over the edge. The work done in pulling the hanging the portion of the chain back to the surface of the table is

a) MgL/n b)MgL/2n

C)MgL/n

^{2 }d)MgL/2n^{2}A pendulum bob of mass 0.1 kg is suspended by a string of 1m long.The bob is displaced so that the string becomes horizontal and released. Find its kinetic energy when the string makes an angle of (i) 0

^{o}, (ii) 30^{o}with the vertical.Q. A particle of mass 0.1 kg is subjected to a force which varies with distance as shown in fig.

If it starts its journey from rest x=0, its velocity at x=12 is

(1) 0 m/s

(2) $\sqrt[20]{3}\text{m/s}$

(3)$\sqrt[20]{2}\text{m/s}$

(4) 40 m/s

(A) PROVE THAT IN CASE OF OBLIQUE ELASTIC COLLISION OF TWO PARTICLES OF SAME MASS IF ONE IS AT REST, AFTER COLLISION BOTH PARTICLES MOVES AT RIGHT ANGLE TO EACH OTHER.

The potential energy of 1kg particle free to move along the x-axis is U(x)=x^4/4-x^2/2 J (x in meters). if the total mechanical energy of the particles is 2J find the maximum speed of the particle.

Q3. two straight lines are drawn on the same displacement time graph make angles 30 degree & 60 degree with time axis respectively which line represents greater velocity ? what is the ratio of the two velocities ?

.

Q. WHAT DO YOU MEAN BY POSITIVE, NEGATIVE AND ZERO WORK DONE. GIVE AT LEAST ONE EXAMPLE OF EACH CASE.

An electric motor is used to lift an elevator and its load (total 1500Kg) to a height of 20

m. The time taken for the job is 20 Sec. The efficiency of the motor is 75%. (i) What isthe work done? (ii) What is the rate at which work is done? (iii) At what rate is theenergy supplied to the motor?9. Two blocks A and B of same mass connected with a spring are placed on a rough inclined plane, which makes an angle $\theta $ with horizontal. What minimu velocity should be given to A up the incline so that B just move ?

$\left(A\right)\sqrt{\frac{m}{K}}\left(g\mathrm{sin}\theta +\mu g\mathrm{cos}\theta \right)\left(B\right)\sqrt{\frac{2m}{K}}\left(g\mathrm{sin}\theta +\mu g\mathrm{cos}\theta \right)\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\left(C\right)\sqrt{\frac{3m}{K}}\left(g\mathrm{sin}\theta +\mu g\mathrm{cos}\theta \right)\left(C\right)\left(A\right)2\sqrt{\frac{m}{K}}\left(g\mathrm{sin}\theta +\mu g\mathrm{cos}\theta \right)$

Is there any formula for inelastic collision??????????????A man pushes a roller with a force of 60N through a distance of 30m.calculate the work done if the handle of the roller is inclined at an angle of 60 with the ground?