COM in Collision and Explosion

Q. A bullet of mass 50g enters a block of thickness t witg speed of 500 m/s.It emerges with 4% of its initial kinetic energy.The emergent speed i

Q.

Blocks of masses $m$, $m,2m,4mand8m$ are arranged in a line on a frictionless floor. Another block of mass $m$, moving with speed $v$ along the same line (see figure) collides with mass m in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass $8m$ starts moving the total energy loss is $p\%$ of the original energy. Value of ‘$p$ is close to:

1. $37$

2. $77$

3. $87$

4. $94$

Q.

A diwali rocket is ejecting 0.05 kg of gases per second at a velocity of 400 m/sec. The accelerating force on the rocket is

1. 20 dynes

2. 22 dynes

3. 20 N

4. 1000 N

Q. 68. A bullet of mass 200g hits a block of thickness 6cm with a speed of 100 m/s . It emerges with 10% of its initial KE . Find its emergent speed.

Q.

The figure shows a block of mass m placed on a smooth wedge of mass M. The value of M' is just sufficient, so that the block of mass m moves vertically downwards with acceleration 10 m/$s^2$_. Chose the correct option:

1. If This is possible then the value of tension in the string is

2. This is possible only for

3. This is possible only for

4. If This is possible then the value of M' is

Q.

Light in certain cases may be considered as a stream of particles called photons. Each photon has a linear momentum $\frac{h}{\lambda }$ where h is the Planck's constant and $\lambda$ is the wavelength of the light. A beam of light of wavelength $\lambda$ is incident on a plane mirror at an angle of incidence $\theta$. Calculate the change in the linear momentum of a photon as the beam is reflected by the mirror.

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Q. A loaded spring gun initially at rest on a horizontalfrictionless surface fires a marble at angle ofelevation e. The mass of the gun is M, the massof the marble is m, and hte muzzle velocity of themarble is vo. The final velocity of the gun isO0000000000 10Mmv cosemVo(2)m+M0a (1)mV0(3)m+Mmvo(4)(m M)Cos emvo sine

Q. 5. A U-238 nucleus originally at rest decays by emitting an -alpha particle say with velocity of v m/s. The recoil velocity (in m/s) of the residual nucleus is

Q. A machine gun has mass of 20kg.It fires 25g bullet at the rate of 600 bullets per minutes with a speed of 200 m/s.Calculate recoil velocity of the gun and force required to keep the gun in position.

Q.

The motion of centre of mass of a system of two particles is unaffected by their internal forces

1. only if they are along the line joining the particles

2. Irrespective of the actual direction of the internal forces

3. only if they are at right angles to the line joining the particles

4. only if they are obliquely inclined to the line joining the particles

Q. 115.A particle of mass m moving towards the east with speed v collides with another particle of same mass and same speed moving towards north. If the two particle stick to each other the new particle of mass 2m will have a speed of: a. v b. v/2 c. v/ root 2 d. v root 2

Q.

Imagine a situation in which the given arrangement is placed inside an elevator that can move only in the vertical direction and compare the situation with the case when it is placed on the ground if the elevator accelerates downward with $a_o$(< g)

1. the limiting friction force between the block M and the surface decreases

2. the tension in the string decreases

3. the system can accelerate with respect to the elevator even when m <

4. the system does not accelerate with respect to the elevator unless m >

Q.

A heavy steel ball of mass greater than 1 kg moving with a speed of 2 $mse{c}^{-1}$collides head on with a stationary ping-pong ball of mass less than 0.1 gm. The collision is elastic. After the collision the ping-pong ball moves approximately with speed

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Q. A bullet has a mass of 0.02 kg and is movingentmewith a speed of 10 m/s. It can penetrate 10 cmof a given target before coming to rest. If thesame target is only 6 cm thick, what will be thespeed and kinetic energy of the bullet, when itcomes out the target?

Q. 76.A bullet of mass 50g is fired from a gun with initial velocity of 35 m per second.if the mass of the gun is 4 kg the recoil velocity of gun will be

Q.

Two balls with masses $m_1$ = 3 kg and $m_2$ = 5 kg have initial velocities $v_1$ = 5 m/s = $v_2$ in the directions as shown in figure. They collide at the origin. Find the velocity of the COM, 3sec before collision?

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Q. A bullet of mass m moving with velocity v strikes a suspended wooden block of mass M . if the block rises to height h , then the initial velocity v of the bullet must have been

Q.

A ball of mass 'm', moving with a velocity 'v' along X-axis, strikes another ball of mass '2m' kept at rest. The first ball comes to rest after collision and the other breaks into two equal pieces. One of the pieces starts moving along Y-axis with a speed $v_1$. What will be the velocity of the other piece?

1. $\sqrt{v^2+v_1^2}$

2. $\sqrt{2v^2+v_1^2}$

3. $\sqrt{v^2-v_1^2}$

4. $\sqrt{\sqrt{v^2+2v_1^2}}$

Q. Sand is being dropped on a conveyor belt at the rate of M Kg/s the force necessary to keep the belt moving with a cons†an t velocity of v m/s will be

Q. 22.a 10g bullet is shot from a 5kg gun with velocity of 400m s what is the speed of the recoil of the gun ?

Q. 92.A bullet of mass 0.02 kg travelling at a speed of 150m/s it can penetrate in box of mass 2 kg . The bullet stop at a distance of 4cm .What should be the velocity of bullet so that it could stop at a distance of 16cm in box ?

Q. 1. What is the law of conservation of linear momentum? 2. What is the law of conservation of angular momentum?

Q.

In the figure shown the cart of mass 6m is initially at rest. A particle of mass m is attached to the end of the light rod which can rotate freely about A. If the rod is released from rest in a horizontal position shown, determine the velocity $v_{rel}$of the particle with respect to the cart when the rod is vertical.

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Q. 8. A machine gun mounted on a 2000 kg car, on a horizontal frictionless surface fires 10 bullets per second. If the mass of each bullet is 10 g and the velocity of each bullet is 500 m/s, then the acceleration of the car will be

Q.

An explosion blows a rock into three parts. Two pieces go off at right angles to each other; 1.0 kg piece with a velocity of 12 m/s and other 2.0 kg piece with a velocity 8 m/s. If the third piece flies off with a velocity 40 m/s, compute the mass of third piece.

1. 1 kg

2. 2 kg

3. kg

4. 0.5 kg

Q. what is scalar and vector quantity ? what z axis ? explain with diagram

Q.

Two masses, nm and m, start simultaneously from the intersection of two straight lines with velocities v and nv respectively. It is observed that the path of their centre of mass is a straight line bisecting the angle between the given straight lines. Find the magnitude of the velocity of centre of mass.[Here $\theta$ = angle between the lines]

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Q. A machine gun fires 50 bullets per second and mass of each bullet is 100g. If 20m/s is the speed of each bullet and mass of gun is 10kg. Magnitude of acceleration of the gun is (1) 10m/s^2 (2) 1m/s^2 (3) 100m/s^2 (4) 0.1m/s^2

Q.

A man of mass M having a bag of mass m slips from the roof of a tall building of height H and starts falling vertically (figure).When at a height h from the ground, he notices that the ground below him is pretty hard, but there is a pond at a horizontal distance x from the line of fall. In order to save himself he throws the bag horizontally (with respect to himself) in the direction opposite to the pond. Calculate the minimum horizontal velocity imparted to the bag so that the man lands in the water.

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Q. 134.A particle of mas m1 moving with velocity v1 collides obliquely with a stationary particle of mass m2. If the particle of mass m1 recoils with a velocity v2 at right angles to its original motion direction find the value of e (coefficient of restitution).