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Syllabus

Prove that newton's second law of motion is the real law

A particle of mass

mmoves with constant speedvon a circular path of radiusr. Find the magnitude of average force on it in half revolution.State and prove law of conservation of linear momentum

m_{1}will remain at rest if:(1) $\frac{1}{{m}_{1}}=\frac{1}{{m}_{2}}+\frac{1}{{m}_{3}}\phantom{\rule{0ex}{0ex}}$ (2) $\frac{{\displaystyle 4}}{{\displaystyle {m}_{1}}}=\frac{{\displaystyle 1}}{{\displaystyle {m}_{2}}}+\frac{{\displaystyle 1}}{{\displaystyle {m}_{3}}}$ (C)

m_{1}=m_{2}+m_{3}(D) $\frac{{\displaystyle 1}}{{\displaystyle {m}_{3}}}=\frac{{\displaystyle 2}}{{\displaystyle {m}_{2}}}+\frac{{\displaystyle 3}}{{\displaystyle {m}_{1}}}$Friction is a necessary evil.Explain

(A) $\u2013\hat{i}$ (B) $-1.8\hat{i}$ (C) $-2.4\hat{i}$ (D) $-3\hat{i}$

State and prove the conservation of angular momentum.

^{2}as shown in figure. The frictional coefficient between the block of mass m and the vehicle so that the block does not fall downwards isQ. A vehicle is moving on a road with an acceleration a = 20 m/s

^{2}as shown in figure. The frictional coefficient between the block of mass m and the vehicle so that the block does not fall downwards isTwo balls A and B are thrown simultaneously ,A vertically upwards with a speed of 20m/s from ground,and B vetically downwards from a height of 40 m with the same seed and along the same line of motion . At what points do the two balls collide ?

a )Mg tan (θ/2)

b) Mg cot (θ/2)

c) Mg sin θ/(1 + sin θ)

d) Mg sin (θ/2)

what are the limitations of dimensional analysis?

A cricket ball of mass 150g is moving with a velocity of 12m/s and is hit by a bat, so that the ball is turned back with a velocity of 20m/s. The force of the blow acts for 0.01s on the ball. Find the average force exerted by the bat on the ball.

a) 0.5

b) 0.6

c) 0.4

d) None of these

D-2. A uniform ladder of length 5m is placed against the wall in vertical plane as shown in the figure. If coefficient of friction $\mu $ is the same for both the wall and the floor then minimum value of $\mu $ for it not to slip is .

(A) $\mu $=1/2 (B) $\mu $=1/4 (C) $\mu $=1/3 (D) $\mu $=1/5

A machine gun has a mass of 20kg. It fires 30g bullets at the rate of 400 bullets per second with a speed of 400 m/s. What force must be applied to the gun to keep it in position ?

A person stands in contaqct against the inner wall of a riotor of radius r The coefficient of friction between the wall and the clothing is u and the rotor is rotating about vertical axis . What is the minimum speed of the rotor so that the person does not slip downward?

show that for two complementary angles of projection of a projectile thrown with thw same velocity. the horizontal ranges are equal

Q4. The value of | T

_{1}– T_{2}| , in the given diagram, isprove Lami's theorem.

trajectory it splits into three segments of masses m, m and 2m. First part falls vertically

downward with zero initial velocity and second part returns via same path to the point of

projection. The velocity of third part of mass 2m just after explosion will be

a) U cos theta b) 3/2 u cos theta c) 2u cos theta d) 5/2 u cos theta

28. If pulleys shown in the diagram are smooth and massless and a

_{ 1}and a2 are acceleration of blocks of mass 4 kg and 8 kg respectively, then(a) a

_{1}= a_{2}(b) a

_{1}= 2a_{2}(c) 2a

_{1}= a_{2}(d) a

_{1}= 4a_{2}Question: On an object of mass 1 kg moving along x-axis with constant speed 8m/s, a constant force 2 N is applied in positive y- direction. Find its speed after 4 seconds.

Please explain how to solve the above question. The answer is 8√2m/s.

1) 10root3 m /s

2) 20root m/s

3) 40/root3 m/s

4) 40 m/s

a block A of mass4 kg is placed on another block B of mass 5kg B rests on smooth table for sliding block A onB a horizontal force of 12 N is required to be applied on A how much max force can be applied on Bso that both A andB move together

1) sin (theta)

2)cos (theta)

3) tan (theta)

4) cot (theta)

A Spring Of Force Constant k is cut into two pieces , such that one piece is doubled the lengthof other . Then the long piece will have a constant of...................?

why cricket player lowers his hands while catching a cricket ball?

a block of mass m is placed on a smooth wedge of inclination theta.the whole system is acclerated horizontally so that the block has a magnitude equal to???

why wheels are made circular in automobiles?

derive an expression for banking of road with the help of diagram?

Q22. Three blocks of masses m

_{1}_{ }= 4kg , m_{2}= 2kg. m_{3}= 4 kg are connected with ideal strings passing over a smooth massless pulley as shown in figure. The acceleration of blocks will be (g = 10 m/s^{2})

How is a friction is a necessary evil?

a stone is dropped from a height h . it hits the ground with a certain momentum P . if the same stone is dropped from a height 100% more than the previous height , the momentum when it hits the ground will change by ??

Why is pulling a lawn roller easier than pushing it?

a) 0.5

b) 0.75

c) 0.57

d) None of these

A small body of mass m slides without friction from the top of a hemisphere of radius r. At what height will the body be detached from the surface of hemisphere?

$\left(1\right)40N\phantom{\rule{0ex}{0ex}}\left(2\right)60N\phantom{\rule{0ex}{0ex}}\left(3\right)80N\phantom{\rule{0ex}{0ex}}\left(4\right)20N$

Q=A ball of mass 20 g hits a wall at an angle of 45^{o}with a velocity of 15 m/s.If the ball rebound at 90^{o}to the direction of incidence ,calculate the impulse received by the ball.wall then magnitude of change in momentum of ball along the wall is

a) 0 b) 2mv c)root3*mv d)mv

define angle and coefficient of friction and find the relationship b/n them.

A man falls on a cemented floor and a man falls on a heap of sand who will get more hurt & why?

Q58. If trolley accelerates horizontally with acceleration a then bob is displaced backward from its initial vertical position. The angular deflection of the bob in equilibrium is

$\left(1\right)\mathrm{\theta}={\mathrm{cos}}^{-1}\left(\frac{\mathrm{a}}{\mathrm{g}}\right)\left(2\right)\mathrm{\theta}={\mathrm{sin}}^{-1}\left(\frac{\mathrm{a}}{\mathrm{g}}\right)\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\left(3\right)\mathrm{\theta}={\mathrm{cot}}^{-1}\left(\frac{\mathrm{a}}{\mathrm{g}}\right)\left(4\right)\mathrm{\theta}={\mathrm{tan}}^{-1}\left(\frac{\mathrm{a}}{\mathrm{g}}\right)$

Three particles each of mass m are situated at the vertices of an equilateral triangle of side a.The only forces acting on the particles are their mutual gravitational forces. It is desired that each particle moves in a circle while maintaining the original mutual seperation a. Find the initial velocity that should be given to each particle and also the time period of the circular motion.

1. A block of mass 10kg is sliding on a surface inclined at a angle of 30

^{0}with the horizontal. Calculate the acceleration of the block. The coefficient of kinetic friction between the block and the surface is 0.5?^{2}which is smaller than acceleration of B then the value of frictional force applied by B on A is:-a) 50N

b) 20N

c) 10N

d) None of these

Kindly answer sir/mam.

how to solve this question with figure 3 blocks r connected together like on a horizontal frictionless table pulled to right with a force=50n if m1=5kg, m2=10kg, m3=15kg. find tension t1 and t2.

2. two masses of 7kg and 12kg r connectd at two end of light inextinsible string that goes over frictionless pulley. find acceleration of mass and tension on the string

ABCDEF is a regular hexagon,,, Prove that AB + AC + AD + AE + AF = 6AO.

(direction sign {--} is present on the top of AB , AC,AD,AE,AF and 6AO)

why friction is called a necessary evil?

_{1}and T_{2}in the strings are (g = 10 m/s^{2}](A) T

_{1}= 8N (B) T_{2}= 36 N (C) T_{1}= 20 N (D) T_{2}= 60 Nprove that impulse is equal to the change in momentum

^{-2}) :-a) 2 m/s

b) 5 m/s

c) 7.2 m/s

d) 9.5 m/s

the motion of a particle of mass m is described by y = ut + 1/2 gt

^{2}. find the force acting on the particle^{2})^{2}towards right. The acceleration of 20 kg mass at this instant is:-a) 12 m/s

^{2}b) 4 m/s

^{2}c) 10 m/s

^{2}d) Zero

state the triangle law of vector addition and the parallelogram law of addition of vectors.

Two blocks of masses 2 kg. and 1 kg. are in contact with each other on a frictionless table . When a horizontal force of 3 N is applied to the block of mass 2 kg. the value of the force of contact between the two block is :(1) 4 N (2) 3N (3) 5 N (4) 1 N

1. prove that angle of repose is equal to angle of friction

2. prove that 2nd law of motion is the real law of motion. (what is real law of motion)

a block of mass 2 kg rests on a rough inclined plane making an angle 30degrees with the horizontal . the coeffecient of static friction between the block and the plane is 0.7 . the frictional force on the block is??

Q27. In the arrangement as shown, tension T

_{2}_{ }is (g = 10 m/s^{2})(1) 50 N (2) 100 N

(3) 50$\sqrt{3}\mathrm{N}$ (4) 100$\sqrt{3}\mathrm{N}$

a circular race track of radius 300 m is banked at an angle of 15

^{0}. if the coefficient of friction between the wheels of a race car and the road is 0.2 , what is the (i) optimum speed of the race car to avoid wear and tear on its tyres (ii) maximum permissible speed to avoid slipping ?plz experts help me out..............

6. A Weightless inextensible rope rests on a stationary wedge forming an angle $\mathrm{\alpha}$ with the horizontal. One end of the rope is fixed to the wall at point A. A small load is attached to the rope at point B, The wedge starts moving to the right with a constant acceleration a. The magnitude of acceleration of the load is given by:

$\left(\mathrm{A}\right)\mathrm{a}\left(\mathrm{B}\right)2\mathrm{a}\mathrm{sin}\frac{\mathrm{a}}{2}\phantom{\rule{0ex}{0ex}}\left(\mathrm{C}\right)\mathrm{a}\mathrm{sin}\mathrm{\alpha}\left(\mathrm{D}\right)\mathrm{g}\mathrm{sin}\mathrm{\alpha}$

a body constrained to move along the z axis of a coordinate system is subjected to a constant force F = ( -i +2j +3k) N . what is the work done by the force in moving the body over a distance of 4 m along the z axis.

^{2}) :-a) 760 N

b) 1360 N

c) 1580 N

d) 1620 N

Kindly answer sir/mam.