iCON Education - Impulse & Momentum JEE Advanced Test

In a scattering experiment, a particle of mass 2m collides with another particle of mass m, which is initially at rest. Assuming the collision to be perfectly elastic, the maximum angular deviation θ of the heavier particle, as shown in the figure, in radians is:

JEE Advanced 2025 Paper 1 Online Physics - Impulse & Momentum Question 1 English

$\tan^{-1}\left(\frac{1}{2}\right)$

A block of mass $5 \mathrm{~kg}$ moves along the $x$-direction subject to the force $F=(-20 x+10) \mathrm{N}$, with the value of $x$ in metre. At time $t=0 \mathrm{~s}$, it is at rest at position $x=1 \mathrm{~m}$. The position and momentum of the block at $t={\pi \over 4} \mathrm{s}$ are

$-0.5 \mathrm{~m}, 5 \mathrm{~kg} \mathrm{~m} / \mathrm{s}$

$0.5 \mathrm{~m}, 0 \mathrm{~kg} \mathrm{~m} / \mathrm{s}$

$0.5 \mathrm{~m},-5 \mathrm{~kg} \mathrm{~m} / \mathrm{s}$

$-1 \mathrm{~m}, 5 \mathrm{~kg} \mathrm{~m} / \mathrm{s}$

A slide with a frictionless curved surface, which becomes horizontal at its lower end, is fixed on the terrace of a building of height $3 h$ from the ground, as shown in the figure. A spherical ball of mass $m$ is released on the slide from rest at a height $h$ from the top of the terrace. The ball leaves the slide with a velocity $\vec{u}_0=u_0 \hat{x}$ and falls on the ground at a distance $d$ from the building making an angle $\theta$ with the horizontal. It bounces off with a velocity $\vec{v}$ and reaches a maximum height $h_1$. The acceleration due to gravity is $g$ and the coefficient of restitution of the ground is $1 / \sqrt{3}$. Which of the following statement(s) is(are) correct?

JEE Advanced 2023 Paper 1 Online Physics - Impulse & Momentum Question 3 English

JEE Advanced 2023 Paper 1 Online Physics - Impulse & Momentum Question 3 English

$\overrightarrow{\mathrm{u}}_0=\sqrt{2 g h} \hat{x}$

$\vec{v}=\sqrt{2 g h}(\hat{x}-\hat{z})$

$d / h_1=2 \sqrt{3}$

One end of a horizontal uniform beam of weight W and length L is hinged on a vertical wall at point O and its other end is supported by a light inextensible rope. The other end of the rope is fixed at point Q, at a height L above the hinge at point O. A block of weight $\alpha$W is attached at the point P of the beam, as shown in the figure (not to scale). The rope can sustain a maximum tension of (2$\sqrt 2 $)W. Which of the following statement(s) is(are) correct?

JEE Advanced 2021 Paper 2 Online Physics - Impulse & Momentum Question 10 English

JEE Advanced 2021 Paper 2 Online Physics - Impulse & Momentum Question 10 English

The vertical component of reaction force at O does not depend on $\alpha$

The horizontal component of reaction force at O is equal to W for $\alpha$ = 0.5

The tension in the rope is 2W for $\alpha$ = 0.5

The rope breaks if $\alpha$ > 1.5

A particle of mass M = 0.2 kg is initially at rest in the xy-plane at a point (x = $-$l, y = $-$h), where l = 10 m and h = 1 m. The particle is accelerated at time t = 0 with a constant acceleration a = 10 m/s² along the positive x-direction. Its angular momentum and torque with respect to the origin, in SI units, are represented by $\overrightarrow L $ and $\overrightarrow \tau $ respectively. $\widehat i$, $\widehat j$ and $\widehat k$ are unit vectors along the positive x, y and z-directions, respectively. If $\widehat k$ = $\widehat i$ $\times$ $\widehat j$ then which of the following statement(s) is(are) correct?

The particle arrives at the point (x = l, y = $-$h) at time t = 2 s

$\overrightarrow \tau = 2\widehat k$ when the particle passes through the point (x = l, y = $-$h)

$\overrightarrow L = 4\widehat k$ when the particle passes through the point (x = l, y = $-$h)

$\overrightarrow \tau = \widehat k$ when the particle passes through the point (x = 0, y = $-$h)

A particle of mass m is projected from the ground with an initial speed u₀ 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 u₀. The angle that the composite system makes with the horizontal immediately after the collision is

${\pi \over 4} + \alpha $

${\pi \over 2} - \alpha $

A particle of mass m is attached to one end of a mass-less spring of force constant k, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time t = 0 with an initial velocity u₀. When the speed of the particle is 0.5 u₀. It collides elastically with a rigid wall. After this collision,

the speed of the particle when it returns to its equilibrium position is u₀.

the time at which the particle passes through the equilibrium position for the first time is $t = \pi \sqrt {{m \over k}} $

the time at which the maximum compression of the spring occurs is $t = {{4\pi } \over 3}\sqrt {{m \over k}} $

the time at which the particle passes through the equilibrium position for the second time is $t = {{5\pi } \over 3}\sqrt {{m \over k}} $

A ball of mass 0.2 kg rests on a vertical post of height 5 m. A bullet of mass 0.01 kg, traveling with a velocity V m/s in a horizontal direction, hits the center of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of 20 m and the bullet at a distance of 100 m from the foot of the post. The velocity V of the bullet is

IIT-JEE 2011 Paper 2 Offline Physics - Impulse & Momentum Question 16 English

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?

Total momentum of the system is 3 kg ms⁻¹

Momentum of 5 kg mass after collision is 4 kg ms⁻¹

Kinetic energy of the centre of mass is 0.75 J

Total kinetic energy of the system is 4 J

Look at the drawing given in the figure below which has been drawn with ink of uniform line-thickness. The mass of ink used to draw each of the two inner circles, and each of the two line segments is $m$. the mass of the ink used to draw the outer circle is $6m$. The coordinates of the centres of the different parts are: outer circle (0, 0), left inner circle ($-a,a$), right inner circle ($a,a$), vertical line (0, 0) and horizontal line ($0,-a$). The y-coordinate of the centre of mass of the ink in this drawing is

IIT-JEE 2009 Paper 1 Offline Physics - Impulse & Momentum Question 7 English

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?

IIT-JEE 2009 Paper 1 Offline Physics - Impulse & Momentum Question 8 English

If collision between the block and the incline is completely elastic, then the vertical (upward) component of the velocity of the block at point B, immediately after it strikes the second incline is

Two balls, having linear momenta ${\overrightarrow p _1} = p\widehat i$ and ${\overrightarrow p _2} = - p\widehat i$, undergo a collision in free space. There is no external force acting on the balls. Let ${\overrightarrow {p'} _1}$ and ${\overrightarrow {p'} _2}$ be their final momenta. The following option(s) is (are) NOT ALLOWED for any non-zero value of $p,{a_1},{a_2},{b_1},{b_2},{c_1}$ and ${c_2}$ :

${\overrightarrow {p'} _1} = {a_1}\widehat i + {b_1}\widehat j + {c_1}\widehat k;{\overrightarrow {p'} _2} = {a_2}\widehat i + {b_2}\widehat j$

${\overrightarrow {p'} _1} = {c_1}\widehat k;{\overrightarrow {p'} _2} = {c_2}\widehat k$

${\overrightarrow {p'} _1} = {a_1}\widehat i + {b_1}\widehat j + {c_1}\widehat k;{\overrightarrow {p'} _2} = {a_2}\widehat i + {b_2}\widehat j - {c_1}\widehat k$

${\overrightarrow {p'} _1} = {a_1}\widehat i + {b_1}\widehat j;{\overrightarrow {p'} _2} = {a_2}\widehat i + {b_1}\widehat j$

Statement 1 :

In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision.

Statement 2 :

In an elastic collision, the linear momentum of the system is conserved.

Statement 1 is True, Statement 2 is True, Statement 2 is a CORRECT explanation for Statement 1

Statement 1 is True, Statement 2 is True, Statement 2 is NOT a CORRECT explanation for Statement 1

Statement 1 is True, Statement 2 is False

Statement 1 is False, Statement 2 is True