Oblique Collision

Q.

What is delta in physics?

Q.

A particle of mass $1kg$ slides down a frictionless track $\left(AOC\right)$ starting from rest at a point $A$ $\left(height2m\right)$. After reaching $C$, the particle continues to move freely in air as a projectile. When it reaches its highest point $P$$\left(height1m\right)$ the kinetic energy of the particle $\left(inJ\right)$ is:(Figure drawn is schematic and not to scale; take $g=10m{s}^{-2}$_____.

Q. In a collinear collision, a particle with an initial speed $v_0$ strikes a stationary particle of the same mass. If the final kinetic energy is $50\%$ greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is

1. $\frac{v_0}{2}$
2. $\frac{v_0}{\sqrt{2}}$
3. $\frac{v_0}{4}$
4. $\sqrt{2}{v}_0$

Q. Two objects of masses, $1\times {10}^{-3}\text{kg}$ and $4\times {10}^{-3}\text{kg}$ have equal momentum. What is the ratio of their kinetic energies?

1. $\text{2:1}$
2. $\text{4:1}$
3. $\text{1:5}$
4. $\text{1:3}$

Q.

A stationary bomb explodes into three pieces. One piece of $2kg$mass moves with a velocity of $8m{s}^{-1}$ at right angles to the other piece of mass $1kg$ moving with a velocity of $12m{s}^{-1}$. If the mass of the third piece is $0.5kg$, then its velocity is

1. $10m{s}^{-1}$

2. $20m{s}^{-1}$

3. $30m{s}^{-1}$

4. $40m{s}^{-1}$

5. $50m{s}^{-1}$

Q. Two identical balls are placed at rest, in contact on a smooth horizontal surface. A third similar ball strikes the two balls symmetrically and comes to rest after the impact. Coefficient of restitution for the collision is (angle between the velocities of moving balls after impact is ${60}^{\circ }$

Q.

A ball is dropped from height 10 m. Ball is embedded in sand 1 m and stops

1. only momentum remains conserved.

2. only kinetic energy remains conserved.

3. both momentum and kinetic energy are conserved.

4. Neither kinetic energy nor momentum is conserved.

Q.

Two balls having masses m and 2m are fastened to two light strings of same length l (figure 9-E18). The other ends of the strings are fixed at O. the strings are kept in the same horizontal line and the system is released from rest. The collision between the balls is elastic. (a) Find the velocities of the balls just after their collision. (b) How high will the balls rise after the collision ?

Q. An alpha particle collides elastically with a stationary nucleus and continues moving at an angle of ${60}^{\circ }$ with respect to the original direction of motion. The nucleus recoils at an angle of ${30}^{\circ }$ with respect to initial direction of motion of alpha particle. Mass number of the nucleus is:

Q.

A spherical ball A of mass $4kg$, moving in a straight line strikes (elastically) another spherical ball B of mass $1kg$ at rest. After the collision, balls A and B move with velocities $V_1$ m/s and $V_2$ m/s respectively, making angles of ${30}^{\circ }$ and ${60}^{\circ }$ with respect to the original direction of motion of A. The ratio $\frac{V_1}{V_2}$ will be:

1. $\frac{\sqrt{3}}{4}$

2. $\frac{4}{\sqrt{3}}$

3. $\frac{1}{\sqrt{3}}$

4. $\sqrt{3}$

Q.

The escape velocity of a particle of mass $\text{m}$varies as

Q.

The horizontal range of a projectile fired at an angle of $15°$ is $50m$. If it is fired with the same speed at an angle of $45°$, its range will be

1. $60m$

2. $71m$

3. $100m$

4. $141m$

Q.

A glass marble whose mass is $200g$ falls from a height of $2.5m$ and rebounds to a height of $1.6m$. Find the change in momentum due to its rebound.

1. $2.54Ns$
2. $4.9Ns$
3. $8.8Ns$
4. $1.57Ns$

Q. What is an inelastic collision?

Q. A particle of mass $m$ moving eastwards with a speed $v$ collides with another particle of same mass moving northwards with same speed $v$. The two particles coalesces on collision. Then, the new particle of mass $2m$ will move with velocity:

1. $\frac{v}{2}\text{North-East}$
2. $\frac{v}{2}\text{North-West}$
3. $\frac{v}{\sqrt{2}}\text{South-West}$
4. $\frac{v}{\sqrt{2}}\text{North-East}$

Q. Which quantity remains conserved in all types of collisions, explain?

Q.

Three guns are aimed at the center of a circle. They are mounted on the circle $120°$ apart. The fire in a timed sequence such that the three bullets collide simultaneously at the center and Combine to form a stationary lump of three bullets. Two of the bullets have masses of $4.5g$ each, and are moving with a speed $v_1\&v_2.$ while the third bullet is having a mass of $2.5g$ and moving with a speed of $575m{s}^{-1}$. Determine the values of $v_1\&v_2.$

Analyze the situation if all the three bullets are having same mass? Same momentum?

Q. A body is projected horizontally from the top of a tower with initial velocity 18 $m{s}^{-1}$. It hits the ground at angle ${45}^{\circ }$. What is the vertical component of velocity when it strikes the ground

1. 
2. 
3. 
4. 

Q. A small steel ball A is suspended by an inextensible thread of length $l=15m$ from O. Another identical ball is thrown vertically downwards such that its surface remains just in contact with thread during downward motion and collides elastically with the suspended ball. If the suspended ball just completes vertical circle after collision, calculate the velocity (in cm/s) of the falling ball just before collision : $(g=10m{s}^{-2})$

Q.

A ball of mass $100g$ moving at a speed of $12m{s}^{-1}$ strikes another ball of mass $200g$ at rest. After the collision both the balls move with common velocity. Find the common velocity.

Q.

A particle of mass 'm' is projected with velocity 'v' an angle $\theta$ with the horizontal. Find its angular momentum about the point of projection when it is at the highest point of its trajectory?

1. along negative z Axis

2. along positive z Axis

3. along negative z Axis

4. along positive z Axis

Q.

A cannon ball is fired with a velocity 200 m/sec at an angle of ${60}^{\circ }$ with the horizontal. At the highest point of its flight it explodes into 3 equal fragments, one going vertically upwards with a velocity 100 m/sec, the second one falling vertically downwards with a velocity 100 m/sec. The third fragment will be moving with a velocity

1. 100 m/s in the horizontal direction

2. 300 m/s in the horizontal direction

3. 200 m/s in a direction making an angle of with the horizontal

4. 300 m/s in a direction making an angle of with the horizontal

Q.

A ball moving with a momentum of $5kgm/s$ strikes against a wall at angle of ${45}^{\circ }$ and is deflected at the same angle. Calculate the change in momentum.

Q. A ball strikes a horizontal floor at an angle ${45}^0$ The value of 'e' between the ball and the floor is 1/2. Find the fraction of K.E. loss during the collision

1. $\frac{5}{8}$
2. $\frac{7}{8}$
3. $\frac{3}{8}$
4. $\frac{3}{4}$

Q. A ball with velocity $9m/s$ collides with another similar stationary ball. After the collision the two balls move in directions making an angle of ${30}^o$ with the initial direction. The ratio of the speeds of balls after the collision will be :

1. $\frac{v_1}{v_2}=1$
2. $\frac{v_1}{v_2}>1$
3. $\frac{v_1}{v_2}<1$
4. $\frac{v_1}{v_2}=0$

Q. If the applied torque is directly proportional to the angular displacement $\theta$, then the work done in rotating the body through an angle $\theta$ would be (C is constant of proportionality).

1. C $\theta$
2. $\frac{1}{2}$C$\theta$
3. $\frac{1}{2}$ C ${\theta }^2$
4. C ${\theta }^2$

Q. A particle of mass m moving with a speed v hits elastically another stationary particle of mass 2 m on a smooth horizontal circular tube of radius r. The time in which the next collision will take place is equal to

1. $\frac{2\pi r}{v}$
2. $\frac{4\pi r}{v}$
3. $\frac{3\pi r}{2v}$
4. $\frac{\pi r}{v}$

Q.

A truck and a car are moving on a smooth, level road such that the kinetic energy associated with them is same. Brakes are applied simultaneously in both of them such that equal retarding forces are produced in them. Which one will cover a greater distance before it stops?

1. Car

2. Truck

3. Both will cover the same distance

4. Nothing can be decided

Q. A ball of mass 3 kg collides with a wall with velocity $10m/sec$ at an angle of ${30}^{\circ }$ with the wall and after collision reflects at the same angle with the same speed. The change in momentum of ball in MKS unit is-

1. 20
2. 45
3. 30
4. 15

Q. A stationary body explodes into two fragments of masses $m_1$ and $m_2$. If momentum of one tangent is $p$, the minimum energy of explosion is

1. $\frac{p^2}{2(m_1+m_2)}$
2. $\frac{p^2}{2\sqrt{m_1{m}_2}}$
3. $\frac{p^2(m_1+m_2)}{2m_1{m}_2}$
4. $\frac{p^2}{2(m_1-m_2)}$