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A jet engine works on the principle of

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Important Questions on Newton's Laws of Motion

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A block of mass m=1 kg slides with velocity v=6 m s-1 on a frictionless horizontal surface and collides with a uniform vertical rod and sticks to it as shown. The rod is pivoted about O and swings as a result of the collision making angle θ before momentarily coming to rest. if the rod has mass M=2 kg, and length =1 m, the value of θ is approximately(take g=10 m s-2

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HARD
A man (mass =50 kg ) and his son (mass =20 kg ) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of 0.70 m s-1 with respect to the man. The speed of the man with respect to the surface is:
MEDIUM
A block of mass m attached to a massless spring is performing oscillatory motion of amplitude 'A' on a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its equilibrium point, the amplitude of oscillation for the remaining system become ƒA. The value of ƒ is:
HARD
An object of mass 5 kg is projected with a velocity 20 m s-1 at an angle 60°, to the horizontal. At the highest point of its path, the projectile explodes and breaks up into two fragments of masses 1 kg and 4 kg. The fragments separate horizontally after the explosion, which releases internal energy such that the KE of the system af the highest point is doubled. The separation between the two fragments when they reach the ground is
HARD

A jeweler is holding a gold chain of uniform mass per unit length hanging vertically just above a weighing scale as shown in the figure. He offers to charge the customer for half of the maximum reading of the scale, after he releases the chain. What percentage more than the actual price does the customer pay if he agrees to the offer?

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HARD
A man holding a rifle (mass of person and rifle together is 100 kg) stands on a smooth surface and fires 10 shots horizontally in 5 sec. Each bullet has a mass 10 g with a muzzle velocity of 800 m s-1. The velocity which the rifle man attains after firing 10 shots will be
EASY
Two particles which are initially at rest move towards each other under the action of their mutual attraction. If their speeds are v and 2v at any instant, then the speed of center of mass of the system is,
MEDIUM

A ball of mass 10 kg moving with a velocity 103 m s-1 along X-axis, hits another ball of mass 20 kg which is at rest. After the collision, the first ball comes to rest and the second one disintegrates into two equal pieces. One of the pieces starts moving along Y-axis at a speed of 10 m s-1. The second piece starts moving at a speed of 20 m s-1 at an angle θ (degree) with respect to the X-axis. The configuration of pieces after the collision is shown in the figure. The value of θ(in degrees) to the nearest integer is _________.

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EASY
A balloon has mass of 10 g in air. The air escapes from the balloon at a uniform rate with velocity 4.5 cm s-1. If the balloon shrinks in 5 s completely. Then, the average force acting on that balloon will be (in dyne).
HARD
A particle of mass m is projected from the ground with an initial speed u at an angle α with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed u. The angle that the composite system makes with the horizontal immediately after the collision is
MEDIUM
A trolley having mass of 200 kg moves with uniform speed of 36 kmh-1 on a frictionless track. A child of mass 20 kg runs on the trolley from one end to the other (10 m away)  with a speed of 4 m s-1 relative to the trolley in a direction opposite to its motion and ultimately jumps out of the trolley. With how much velocity has the trolley moved from the time the child begins to run?
MEDIUM
A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate dMtdt=bv2t, where vt is its instantaneous velocity. The instantaneous acceleration of the satellite is:
MEDIUM
A stationary body explodes into two parts of masses M1 and M2. They move in opposite directions with velocities v1 and v2. The ratio of their kinetic energies is
MEDIUM
Given the masses of various atomic particles mP=1,0072umn=1,0087ume=0.000548umv¯=0md=2.0141u, where p=proton, nneutron, eelectron, v¯antineutrino and d¯deuteron. Which of the following process is allowed by momentum and energy conservation :
MEDIUM
A bomb of mass 18 kg at rest explodes into two pieces of masses 6 kg and 12 kg. The velocity of 12 kg mass is 4 m/s. The kinetic energy of the other mass is
EASY

A ball of mass 10 kg moving with a velocity 103 m s-1 along the x -axis, hits another ball of mass 20 kg which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along y -axis with a speed of 10 m s-1. The second piece starts moving at an angle of 30° with respect to the x -axis. The velocity of the ball moving at 30° with x -axis is x m s-1. The configuration of pieces after the collision is shown in the figure below. The value of x to the nearest integer is

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EASY
An object of mass m1 collides with another object of mass m2, which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses m2:m1 is :
MEDIUM
A body of mass 4m is lying in x - y plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass m move perpendicular to each other with equal speeds υ. The total kinetic energy generated due to explosion is:
EASY
A balloon has a mass of 10 gram in air. The air escapes from the balloon at a uniform rate with a velocity of 5 cm s-1 and the balloon shrinks completely in 2.5 s. The average force acting on the balloon will be
EASY
A 5000 kg rocket is set for vertical firing. The exhaust speed is  800ms1.  To give an initial upward acceleration of 20 m s-2, the amount of gas ejected per second to supply the needed thrust will be:  g=10ms2