A body A of mass m is moving in a circular orbit of radius R about a planet. Another body B of mass m 2 collides with A with a velocity which is half v → 2 the instantaneous velocity v → of A. The collision is completely inelastic. Then, the combined body:

starts moving in an elliptical orbit around the planet

continues to move in a circular orbit

Escapes from the Planet's Gravitational field

Falls vertically downwards towards the planet

EASY

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Linear momentum is always conserved in an inelastic collision.

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Important Questions on Laws of Motion

MEDIUM

Physics>Mechanics>Laws of Motion>Collisions

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 $ν$ collides with stationary point particle of mass $M$ . If the maximum energy loss possible is given as
$f (\frac{1}{2} m ν^{2})$ then $f = (\frac{m}{M + m})$ .

$Statement - II:$ Maximum energy loss occurs when the particles get stuck together as a result of the collision.

EASY

Physics>Mechanics>Laws of Motion>Collisions

A ball is thrown vertically downwards from a height of

20 m

with an initial velocity

v_{0}

. It collides with the ground, loses

50

percent of its energy in collision and rebounds to the same height. The initial velocity

v_{0}

is: (Take

g = 10 m s^{- 2}

)

MEDIUM

Physics>Mechanics>Laws of Motion>Collisions

A body of mass

2 k g

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?

HARD

Physics>Mechanics>Laws of Motion>Collisions

An alpha- particle of mass

m

suffers

1 -

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

HARD

Physics>Mechanics>Laws of Motion>Collisions

It is found that if a neutron suffers an elastic collinear collision with a deuterium at rest, the fractional loss of its energy is

P_{d}

, while for its similar collision with a carbon nucleus at rest, the fractional loss of energy is

P_{c}

. The values of

P_{d}

and

P_{c}

are respectively

HARD

Physics>Mechanics>Laws of Motion>Collisions

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 ≪ \frac{d L}{L} v_{0},

where

d L

is the infinitesimal displacement of the piston. Which of the following statement(s) is/are correct?

Question Image

EASY

Physics>Mechanics>Laws of Motion>Collisions

A body of mass

m_{1}

moving with an unknown velocity of

v_{1} \hat{i},

undergoes a collinear collision with a body of mass

m_{2}

moving with a velocity

v_{2} \hat{i} .

After the collision,

m_{1}

and

m_{2}

move with velocities of

v_{3} \hat{i}

and

v_{4} \hat{i},

respectively. If

m_{2} = 0.5 m_{1}

and

v_{3} = 0.5 v_{1},

then

v_{1}

is:

MEDIUM

Physics>Mechanics>Laws of Motion>Collisions

A body A of mass

m

is moving in a circular orbit of radius

R

about a planet. Another body B of mass

\frac{m}{2}

collides with A with a velocity which is half

(\frac{\vec{v}}{2})

the instantaneous velocity

\vec{v}

of A. The collision is completely inelastic. Then, the combined body:

HARD

Physics>Mechanics>Laws of Motion>Collisions

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 the collision, is

HARD

Physics>Mechanics>Laws of Motion>Collisions

A body

A

of mass

m = 0.1 k g

has an initial velocity of

3 \hat{i} m s^{- 1}

. It collides elastically with another body

B

of the same mass which has an initial velocity of

5 \hat{j} m s^{- 1}

. After the collision,

A

moves with a velocity

\vec{v} = 4 (\hat{i} + \hat{j}) m s^{- 1}

. The energy of

B

after the collision is written as

\frac{x}{10} J

. The value of

x

MEDIUM

Physics>Mechanics>Laws of Motion>Collisions

A particle of mass

m

is moving with speed

2 v

and collides with a mass

2 m

moving with speed

v

in the same direction. After the collision, the first mass is stopped completely while the second one splits into two particles each of mass

m,

which move at an angle

45^{o}

with respect to the original direction. The speed of each of the moving particle will be

HARD

Physics>Mechanics>Laws of Motion>Collisions

An oscillator of mass

M

is at rest in its equilibrium position in a potential,

V = \frac{1}{2} k {(x - X)}^{2}

. A particle of mass

m

comes from the right with speed

u

and collides completely inelastic with

M

and sticks to it. This process repeats every time the oscillator crosses its equilibrium position. The amplitude of oscillations after

13

collisions is:

(M = 10, m = 5, u = 1, k = 1)

MEDIUM

Physics>Mechanics>Laws of Motion>Collisions

Two particles of masses $M$ and $2 M$ are moving with speeds of $10 m s^{- 1}$ and $5 m s^{- 1}$ , as shown in the figure. They collide at the origin and after that they move along the indicated directions with speeds $v_{1}$ and $v_{2}$ , respectively. The values of $v_{1}$ and $v_{2}$ are, nearly
Question Image

HARD

Physics>Mechanics>Laws of Motion>Collisions

A simple pendulum, 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 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:

EASY

Physics>Mechanics>Laws of Motion>Collisions

A block of mass

m

moving on a frictionless surface at speed

v

collides elastically with a block of same mass, initially at rest. Now the first block moves at an angle

θ

with its initial direction and has speed

v_{1}

. The speed of the second block after the collision is

HARD

Physics>Mechanics>Laws of Motion>Collisions

A particle of mass m is projected with a speed u from the ground at an angle

θ = \frac{π}{3}

w.r.t. horizontal (x-axis). When it has reached its maximum height, it collides completely inelastically with another particle of the same mass and velocity

u \hat{i} .

The horizontal distance covered by the combined mass before reaching the ground is:

MEDIUM

Physics>Mechanics>Laws of Motion>Collisions

Two particles of equal mass

m

have respective initial velocities

u \hat{i}

and

u (\frac{\hat{i} + \hat{j}}{2})

. They collide completely inelastically. The energy lost in the process is:

MEDIUM

Physics>Mechanics>Laws of Motion>Collisions

Body

A

of mass

4 m

moving with speed

u

collides with another body

B

of mass

2 m

at rest. The collision is head on and elastic in nature. After the collision, the fraction of energy lost by the colliding body

A

EASY

Physics>Mechanics>Laws of Motion>Collisions

Two identical balls

A

and

B

having velocities of

0.5 m s^{- 1}

and

- 0.3 m s^{- 1}

, respectively, collide elastically in one dimension. The velocities of

B

and

A

after the collision, respectively, will be

HARD

Physics>Mechanics>Laws of Motion>Collisions

A large number $(n)$ of identical beads, each of mass $m$ and radius $r$ are strung on a thin smooth rigid horizontal rod of length $L (L ≫ r)$ and are at rest at random positions. The rod is mounted between two rigid supports (see figure). If one of the beads is now given a speed $v$ , the average force experienced by each support after a long time is (assume all collisions are elastic):
Question Image

Linear momentum is always conserved in an inelastic collision.

Important Questions on Laws of Motion

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