COM in Collision and Explosion

Q.

Prove that Newtons second law of motion is the only real law of motion.

Q. A mass $m$ moves in a circle on a smooth horizontal plane with velocity $v_0$ at a radius $R_0$. The mass is attached to a string which passes through a smooth hole in the plane as shown.


The tension in the string is increased gradually and finally $m$ moves in a
circle of radius $R_0/2$. Then, the final value of the kinetic energy of particle is

1. $\frac{1}{2}m{v_0}^2$
2. $m{v_0}^2$
3. $\frac{1}{4}m{v_0}^2$
4. $2m{v_0}^2$

Q. What is recoil velocity of a gun? How can you derive the expression for recoil velocity of gun?

Q.

A particle moves in the x – y plane under the influence of a force such that its linear momentum is $p\left(t\right)=A\left[\hat{i}cos\right(kt)-\hat{j}sin(kt\left)\right]$, where A and k are constants. The angle between the force and the momentum is

1. $0^{\circ }$

2. ${90}^{\circ }$

3. ${45}^{\circ }$

4. ${30}^{\circ }$

Q.

A particle of mass m moving in the x-direction with speed 2v is hit by another particle of mass 2m moving in the y-direction with speed v. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to

1. 50%

2. 56%

3. 62%

4. 44%

Q.

Which factors are most important in projectile motion?

Q. A swimmer wants to cross a river from point $A$ to point $B$. Line $AB$ makes an angle of ${30}^{\circ }$ with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle $\theta$ with the line $AB$ sholud be $x^{\circ }$ , so that the swimmer reaches point $B.$ The value of $x$ is

Q.

A particle of mass m is projected from the ground with an initial speed $u_0$ at an angle $\alpha$ 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 $u_0$. The angle that the composite system makes with the horizontal immediately after the collision is ?

1. $\frac{\pi }{4}$

2. $\frac{\pi }{4}+\alpha$

3. $\frac{\pi }{4}-\alpha$

4. $\frac{\pi }{2}$

Q. Light is incident normally on a completely absorbing surface with an energy flux of $25{\text{Wcm}}^{-2}$. If the surface has an area of $25{\text{cm}}^2,$ the momentum transferred to the surface in $40\text{min}$ time duration will be:

1. $1.4\times {10}^{-6}\text{Ns}$
2. $3.5\times {10}^{-6}\text{Ns}$
3. $5.0\times {10}^{-3}\text{Ns}$
4. $6.3\times {10}^{-4}\text{Ns}$

Q. In figure a solid ball rolls smoothly from rest $($starting at height $H=6.0\text{m})$ until it leaves the horizontal section at the end of the track, at height $h=2.0\text{m}$. The ball hit the ground at distance $x\text{m}$ horizontally from point $A$. Find the value of $x$.

$[$ Take $g=10{\text{m/s}}^2$$]$

Q.

A particle of mass $200\raisebox{1ex}{$MeV$}\!\left/ \!\raisebox{-1ex}{$c^2$}\right.$ collides with a hydrogen atom at rest. Soon after the collision, the particle comes to rest, and the atom recoils and goes to its first excited state. The initial kinetic energy of the particle $\left(ineV\right)$ is $\raisebox{1ex}{$N$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$. The value of $N$ is : (Given the mass of the hydrogen atom to be $1\raisebox{1ex}{$GeV$}\!\left/ \!\raisebox{-1ex}{$c^2$}\right.$)

Q. A ball is dropped from height $h$ on a floor. If the coefficient of restitution is $e$, find the total distance covered by the ball before coming to rest on the ground.

1. $\left(\frac{1-e}{1+e}\right)h$
2. $\left(\frac{1+e}{1-e}\right)h$
3. $\left(\frac{1-e^2}{1+e^2}\right)h$
4. $\left(\frac{1+e^2}{1-e^2}\right)h$

Q. A bomb at rest explodes into three equal fragments. Two fragments fly off at right angles with velocity $12\text{m/s}$ and $9\text{m/s}$. If the explosion process occurs in $0.1\text{s}$, find out the average force acting on the third particle, if total mass of the bomb is $12\text{kg}$.

1. $600\text{N}$
2. $60\text{N}$
3. $15\text{N}$
4. $1200\text{N}$

Q. A boy of mass $50\text{kg}$ jumps to a height of $0.8\text{m}$ from the ground, then momentum transferred by the ground to the boy is -

1. $400\text{kg-m/s}$
2. $200\text{kg-m/s}$
3. $800\text{kg-m/s}$
4. $500\text{kg-m/s}$

Q. Calculate the impulse necessary to stop a 1500 kg car travelling at 90 km per hr.

Q. machine gun fires 10 bullets/s, each of mass 10g, the speed of each bullet is 20 cm/s, then force of recoil is:

Q. A person falling on the cemented floor is injured more than the person falling on the heap of sand. Why?

Q.

Newton's second law gives the measure of

1. Acceleration

2. Force

3. Momentum

4. Angular momentum

Q. $n\times {10}^{27}$ photons of wavelength $\lambda =6600\text{nm}$ must strike a totally reflecting surface per second at normal incidence to exert a force of $1\text{N}.$ The value n is (integer only)

Q. A projectile of mass $2\text{m}$ explodes at the highest point of its path. It breaks into two equal parts. One part retraces its path. Find the distance of the second part from the point of projection when it finally lands on the ground. Given that range of the projectile would be $200\text{m}$ if no explosion had taken place.

1. $100\text{m}$
2. $400\text{m}$
3. $200\text{m}$
4. $150\text{m}$

Q.

A stone of mass m tied to the end of a string revolves in a vertical circle of radius R. The net forces at the lowest and highest points of the circle directed vertically downwards are: [Choose the correct alternative]

	Lowest Point	Highest Point
(a)	mg – T1	mg + T2
(b)	mg + T1	mg – T2
(c)	mg + T1 –/R	mg – T2 + /R
(d)	mg – T1 – /R	mg + T2 + /R

T₁ and v₁ denote the tension and speed at the lowest point. T₂ and v₂ denote corresponding values at the highest point.

Q.

A machine gun fires a bullet of mass of 65 g with a velocity of 1300 m/s. The man holding it can exert a maximum force of 169 N on the gun. What will be the number of bullets he can fire per second?

Q. A motor car running at he rate of 7ms-1 can be stopped by applying brakes in 10m. Show that total resistance to the motion, when the brakes are on, is one fourth of the weight of the car.

Q.

A machine gun fires A bullet of mass 40 gram with the velocity of 1200m/s. The gun can exert a maximum force of 144N on the bullet. How many bullets can it fire per second at the most?

Q.

A bullet of mass 20 g moving horizontally at a speed of 300 m/s is fired into a wooden block of mass 500 g suspended by a long string.The bullet crosses the block and emerges on the other side.If the centre of mass of the block rises through a height of 20.0 cm, find the speed of the bullet as it emerges from the block.

Q.

The moment of inertia of a system of four rods, each of length l and mass m, about the axis shown is

1. 

2. 

3. 

4. 

Q.

Can a body have momentum without having kinetic energy?

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 below 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.If the man just succeeds to avoid the hard ground, where will the bag land?

Q. A child is sitting on a swing. Its minimum and maximum heights from the ground are $0.75\text{m}$ and $2\text{m}$ respectively, its maximum speed will be

1. $\text{15 m/s}$
2. $\text{10 m/s}$
3. $\text{8 m/s}$
4. $\text{5 m/s}$

Q. Force$\left(F\right)$ - time$\left(t\right)$ graph is given below. Calculate the impulse experienced by the body.

1. $5000\text{N-s}$
2. $6000\text{N-s}$
3. $4500\text{N-s}$
4. $3500\text{N-s}$