Head-on Collision

Interactive Feed

JEE Main 2019, 9 April Shift-I

LEVELJEE Main

A body of mass 2 kg makes an elastic collision with a second body at rest and continues to move in the original direction but with one-fourth of its original speed. What is the mass of the second body?

Blocks of masses $m, 2 m, 4 m$ and $8 m$ 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 $8 m$ starts moving, the total energy loss is $p %$ of the original energy. Value of $p$ is close to

JEE Main 2019, 10 Jan Shift-I

LEVELJEE Advanced

A piece of wood of mass $0.03 kg$ is dropped from the top of a $100 m$ height building. At the same time, a bullet of mass $0.02 kg$ is fired vertically upward with a velocity $100 ms^{- 1}$ from the ground. The bullet gets embedded in the wood. Then, the maximum height to which the combined system reaches above the top of the building before falling below is (Take, $g = 10 ms^{- 2}$ )

A block of mass $0.50 kg$ is moving with a speed of $2.00 ms^{- 1}$ on a smooth surface. It strikes another mass of $1.00 kg$ and then they move together as a single body. The energy loss during the collision is

(A)

0.16 J

(B)

1.00 J

(C)

0.67 J

(D)

0.34 J

JEE Main 2019, 9 Jan Shift-I

LEVELJEE Main

Three blocks $A, B$ and $C$ are lying on a smooth horizontal surface as shown in the figure. $A$ and $B$ have equal masses $m$ while $C$ has mass $M$ . Block $A$ is given an initial speed $v$ towards $B$ due to which it collides with $B$ perfectly inelastically. The combined mass collides with $C$ , also perfectly inelastically $\frac{5}{6}$ th of the initial kinetic energy is lost in whole process. What is value of $\frac{M}{m}$ ?

JEE Main 2021, 27 July Shift-I

LEVELJEE Main

Three objects $A, B$ and $C$ are kept in a straight line on a frictionless horizontal surface. The masses of $A, B$ and $C$ are $m, 2 m$ and $2 m$ , respectively. $A$ moves towards $B$ with a speed of $9 m/s$ and makes an elastic collision with it. There after $B$ makes a completely inelastic collision with $C$ . All motions occur along same straight line. The final speed of $C$ is

(A)

6 m/s

(B)

9 m/s

(C)

4 m/s

(D)

3 m/s

JEE Main 2019, 12 Jan Shift-II

LEVELJEE Main

An $α$ -particle of mass $m$ suffers one-dimensional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing 64% of its initial kinetic energy. The mass of the nucleus is

JEE Main 2021, 17 March Shift-II

LEVELJEE Advanced

A rubber ball is released from a height of $5 m$ above the floor. It bounces back repeatedly, always rising to $\frac{81}{100}$ of the height through which it falls. Find the average speed of the ball. (Take, $g = 10 ms^{- 2}$ )

(A)

3.0 ms^{- 1}

(B)

3.5 ms^{- 1}

(C)

2.0 ms^{- 1}

(D)

2.5 ms^{- 1}

JEE Main 2019, 12 Jan Shift-I

LEVELJEE Advanced

A simple pendulum is made of a string of length $l$ and a bob of mass $m$ , is released from a small angle $θ_{0}$ . It strikes a block of mass $M$ , kept on a horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle $θ_{1}$ . Then, $M$ is given by

(A)

m (\frac{θ _{0} + θ _{1}}{θ _{0} - θ _{1}})

(B)

\frac{m}{2} (\frac{θ _{0} - θ _{1}}{θ _{0} + θ _{1}})

(C)

m (\frac{θ _{0} - θ _{1}}{θ _{0} + θ _{1}})

(D)

\frac{m}{2} (\frac{θ _{0} + θ _{1}}{θ _{0} - θ _{1}})

JEE Main 2013

LEVELJEE Main

This question has Statement I and Statement II. Of the four choices given after the statements, choose the one that best describes the two statements. Statement I A point particle of mass $m$ moving with speed $v$ collides with stationary point particle of mass $M$ . If the maximum energy loss possible is given as $f (\frac{1}{2} m v^{2})$ , then $f = (\frac{m}{M + m})$ . Statement II Maximum energy loss occurs when the particles get stuck together as a result of the collision.

(A)

Statement I is true, Statement II is true; Statement II is the correct explanation of Statement I

(B)

Statement I is true, Statement II is true; Statement II is not the correct explanation of Statement I

(C)

Statement I is true, Statement II is false

(D)

Statement I is false, Statement II is true

JEE Main 2021, 26 Feb Shift-I

LEVELJEE Main

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion (A) Body $P$ having mass $M$ moving with speed $u$ has head-on collision elastically with another body $Q$ having mass $m$ initially at rest. If $m ≪ M$ , body $Q$ will have a maximum speed equal to $2 u$ after collision. Reason (R) During elastic collision, the momentum and kinetic energy are both conserved. In the light of the above statements, choose the most appropriate answer from the options given below.

(A)

A is not correct but R is correct.

(B)

Both A and R are correct but R is not the correct explanation of A.

(C)

Both A and R are correct and R is the correct explanation of A.

(D)

A is correct but R is not correct.

JEE Main 2018

LEVELJEE Advanced

In a collinear collision, a particle with an initial speed $v_{0}$ strikes a stationary particle of the same mass. If the final total kinetic energy is $50%$ greater than the original kinetic energy, the magnitude of the relative velocity between the two particles after collision, is

(A)

\frac{v _{0}}{4}

(B)

2 v_{0}

(C)

\frac{v _{0}}{2}

(D)

\frac{v _{0}}{2}

JEE Main 2021, 18 March Shift-II

LEVELJEE Main

An object of mass $m_{1}$ collides with another object of mass $m_{2}$ , which is at rest. After the collision, the objects move with equal speeds in opposite direction. The ratio of the masses $m_{2} : m_{1}$ is

JEE Main 2020, 8 Jan Shift-II

LEVELJEE Advanced

A particle of mass $m$ is dropped from a height $h$ above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of $2 g h$ . If they collide head-on completely inelastically, then the time taken for the combined mass to reach the ground, in units of $\frac{h}{g}$ is

(A)

\frac{1}{2}

(B)

\frac{1}{2}

(C)

\frac{3}{2}

(D)

\frac{3}{4}

JEE Main 2021, 25 July Shift-1

LEVELJEE Advanced

A body of mass $2 kg$ moving with a speed of $4 m/s$ makes an elastic collision with another body at rest and continues to move in the original direction but with one-fourth of its initial speed. The speed of the two body centre of mass is $\frac{x}{10} m/s$ . Then, the value of $x$ is ......... .

JEE Advanced 1993

LEVELJEE Advanced

Two blocks $A$ and $B$ each of mass $m$ , are connected by a massless spring of natural length $L$ and spring constant $k$ . The blocks are initially resting on a smooth horizontal floor with the spring at its natural length, as shown in figure. A third identical block $C$ , also of mass $m$ , moves on the floor with a speed $v$ along the line joining $A$ and $B$ , and collides elastically with $A$ . Then

* Multiple Correct Options

(A)

the kinetic energy of the

A

B

system, at maximum compression of the spring, is zero

(B)

the kinetic energy of the

A

B

system, at maximum compression of the spring, is

\frac{m v ^{2}}{4}

(C)

the maximum compression of the spring is

v \frac{m}{k}

(D)

the maximum compression of the spring is

v \frac{m}{2 k}

JEE Advanced (2009)

LEVELJEE Main

Two small particles of equal masses start moving in opposite directions from a point $A$ in a horizontal circular orbit. Their tangential velocities are $v$ and $2 v$ respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at $A$ , these two particles will again reach the point $A$ ?

This question has statement I and statement II. Of the four choices given after the statements, choose the one that best describes the two statements. Statement I A point particle of mass $m$ moving with speed $v$ collides with stationary point particle of mass $M$ . If the maximum energy loss possible is given as $f (\frac{1}{2} m v^{2})$ , then $f = (\frac{m}{M + m})$ . Statement II Maximum energy loss occurs when the particles get stuck together as a result of the collision.

(A)

Statement I is true, Statement II is true, and Statement II is the correct explanation of Statement I

(B)

Statement I is true, Statement II is true, but Statement II is not the correct explanation of Statement I

(C)

Statement I is true, Statement II is false

(D)

Statement I is false, Statement II is true

JEE Advanced 2009

LEVELJEE Main

Three objects $A, B$ and $C$ are kept in a straight line on a frictionless horizontal surface. These have masses $m, 2 m$ and $m$ , respectively. The object $A$ moves towards $B$ with a speed $9 ms^{- 1}$ and makes an elastic collision with it. Thereafter, $B$ makes completely inelastic collision with $C$ . All motions occur on the same straight line. Find the final speed (in $ms^{- 1}$ ) of the object $C$ .

JEE Advanced 1987

LEVELJEE Advanced

A simple pendulum is suspended from a peg on a vertical wall. The pendulum is pulled away from the wall to a horizontal position (see fig.) and released. The ball hits the wall, the coefficient of restitution being $\frac{2}{5}$ . What is the minimum number of collisions after which the amplitude of oscillations becomes less than $6 0^{\circ}$ ?

JEE Advanced (1984)

LEVELJEE Advanced

Two bodies $A$ and $B$ of masses $m$ and $2 m$ respectively are placed on a smooth floor. They are connected by a spring. A third body $C$ of mass $m$ moves with velocity $v_{0}$ along the line joining $A$ and $B$ and collides elastically with $A$ as shown in figure. At a certain instant of time $t_{0}$ after collision, it is found that the instantaneous velocities of $A$ and $B$ are the same. Further at this instant the compression of the spring is found to be $x_{0}$ . Determine (a) the common velocity of $A$ and $B$ at time $t_{0}$ and (b) the spring constant.

JEE Advanced (2010)

LEVELJEE Main

A point mass of $1 kg$ collides elastically with a stationary point mass of $5 kg$ . After their collision, the $1 kg$ mass reverses its direction and moves with a speed of $2 ms^{- 1}$ . Which of the following statement(s) is/are correct for the system of these two masses?

* Multiple Correct Options

(A)

(a) Total momentum of the system is

3 kg-ms^{- 1}

(B)

(b) Momentum of

5 kg

mass after collision is

4 kg-ms^{- 1}

(C)

0.75 J

(D)

(d) Total kinetic energy of the system is

4 J

JEE Advanced 1998

LEVELJEE Advanced

A wedge of mass $m$ and triangular cross-section ( $A B = B C = C A = 2 R$ ) is moving with a constant velocity ( $- v \hat{i}$ ) towards a sphere of radius $R$ fixed on a smooth horizontal table as shown in the figure. The wedge makes an elastic collision with the fixed sphere and returns along the same path without any rotation. Neglect all friction and suppose that the wedge remains in contact with the sphere for a very short time $Δ t$ during which the sphere exerts a constant force $F$ on the wedge. (a) Find the force $F$ and also the normal force $N$ exerted by the table on the wedge during the time $Δ t$ . (b) Let $h$ denote the perpendicular distance between the centre of mass of the wedge and the line of action of $F$ . Find the magnitude of the torque due to the normal force $N$ about the centre of the wedge during the interval $Δ t$ .

JEE Advanced 1999

LEVELJEE Advanced

Two blocks of masses $2 kg$ and $M$ are at rest on an inclined plane and are separated by a distance of $6.0 m$ as shown. The coefficient of friction between each block and the inclined plane is $0.25$ . The $2 kg$ block is given a velocity of $10.0 m/s$ up the inclined plane. It collides with $M$ , comes back and has a velocity of $1.0 m/s$ when it reaches its initial position. The other block $M$ after the collision moves $0.5 m$ up and comes to rest. Calculate the coefficient of restitution between the blocks and the mass of the block $M$ . [Take $sin θ \approx tan θ = 0.05$ and $g = 10 m/s^{2}$ ]

JEE Advanced 2019

LEVELJEE Advanced

A small particle of mass $m$ moving inside a heavy, hollow and straight tube along the tube axis undergoes elastic collision at two ends. The tube has no friction and it is closed at one end by a flat surface while the other end is fitted with a heavy movable flat piston as shown in figure. When the distance of the piston from closed end is $L = L_{0}$ the particle speed is $v = v_{0}$ . The piston is moved inward at a very low speed $V$ such that $V ≪ v_{0}$ , where $d L$ is the infinitesimal displacement of the piston. Which of the following statement(s) is/are correct? [JEE(Advanced) 2019]

* Multiple Correct Options

(A)

The rate at which the particle strikes the piston is

v / L

(B)

After each collision with the piston, the particle speed increases by

2 V

(C)

The particle's kinetic energy increases by a factor of 4 when the piston is moved inward from

L_{0}

\frac{1}{2} L_{0}

(D)

If the piston moves inward by

d L

, the particle speed increases by

2 v \frac{d L}{L}