Given the masses of various atomic particles m P = 1 , 0072 u , m n = 1 , 0087 u , m e = 0 .000548 u , m v ¯ = 0 , m d = 2 .0141 u , where p = proton, n ≡ neutron, e ≡ electron, v ¯ ≡ antineutrino and d ¯ ≡ deuteron. Which of the following process is allowed by momentum and energy conservation :

n + n → deuterium atom (electron bound to the nucleus)

HARD

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A flat car of mass $M$ is at rest on a frictionless floor with a child of mass m standing at the edge. If the child jumps off from the car towards right with initial velocity $u$ , with respect to car, find the velocity of car after the jump.

Important Questions on Systems of Particles and Rotational Motion

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Linear Momentum of a System of Particles

A body of mass

M

moving with velocity

v

explodes into two equal parts. If one part comes to rest and the other part moves with velocity

v_{0}

; what would be the value of

v_{0}

HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Linear Momentum of a System of Particles

A man holding a rifle (mass of person and rifle together is

100 kg

) stands on a smooth surface and fires

10

shots horizontally in

5 \sec

. Each bullet has a mass

10 g

with a muzzle velocity of

800 m s^{- 1} .

The velocity which the rifle man attains after firing

10

shots will be

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Linear Momentum of a System of Particles

A trolley having mass of

200 kg

moves with uniform speed of

36 {kmh}^{- 1}

on a frictionless track. A child of mass

20 kg

runs on the trolley from one end to the other (

10 m

away) with a speed of

4 m s^{- 1}

relative to the trolley in a direction opposite to its motion and ultimately jumps out of the trolley. With how much velocity has the trolley moved from the time the child begins to run?

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Linear Momentum of a System of Particles

A bomb of mass

18 kg

at rest explodes into two pieces of masses

6 kg

and

12 kg .

The velocity of

12 kg

mass is

4 m / s .

The kinetic energy of the other mass is

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Linear Momentum of a System of Particles

Two particles which are initially at rest move towards each other under the action of their mutual attraction. If their speeds are

v

and

2 v

at any instant, then the speed of center of mass of the system is,

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Linear Momentum of a System of Particles

Two particles of masses

m_{1}

and

m_{2}

have equal kinetic energies. The ratio of their momentum is:

HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Linear Momentum of a System of Particles

An object of mass

5 kg

is projected with a velocity

20 m s^{- 1}

at an angle

60 °

, to the horizontal. At the highest point of its path, the projectile explodes and breaks up into two fragments of masses

1 kg

and

4 kg .

The fragments separate horizontally after the explosion, which releases internal energy such that the

K E

of the system af the highest point is doubled. The separation between the two fragments when they reach the ground is

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Linear Momentum of a System of Particles

A block moving horizontally on a smooth surface with a speed of

40 m s^{- 1}

splits into two parts with masses in the ratio of

1 : 2 .

If the smaller part moves at

60 m s^{- 1}

in the same direction, then the fractional change in kinetic energy is :

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Linear Momentum of a System of Particles

A block of mass m attached to a massless spring is performing oscillatory motion of amplitude 'A' on a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its equilibrium point, the amplitude of oscillation for the remaining system become ƒA. The value of ƒ is:

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Linear Momentum of a System of Particles

A block of mass $m = 1 kg$ slides with velocity $v = 6 m s^{- 1}$ on a frictionless horizontal surface and collides with a uniform vertical rod and sticks to it as shown. The rod is pivoted about $O$ and swings as a result of the collision making angle $θ$ before momentarily coming to rest. if the rod has mass $M = 2 kg,$ and length $ℓ = 1 m,$ the value of $θ$ is approximately $(take g = 10 m s^{- 2})$

Question Image

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Linear Momentum of a System of Particles

A ball of mass $10 kg$ moving with a velocity $10 \sqrt{3} {m s}^{- 1}$ along $X$ -axis, hits another ball of mass $20 kg$ which is at rest. After the collision, the first ball comes to rest and the second one disintegrates into two equal pieces. One of the pieces starts moving along $Y$ -axis at a speed of $10 m s^{- 1}$ . The second piece starts moving at a speed of $20 m s^{- 1}$ at an angle $θ$ (degree) with respect to the $X$ -axis. The configuration of pieces after the collision is shown in the figure. The value of $θ$ (in degrees) to the nearest integer is _________.

Question Image

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Linear Momentum of a System of Particles

A ball is thrown vertically up (taken as

+ z - a x i s

) from the ground. The correct momentum-height

(p - h)

diagram is:

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Linear Momentum of a System of Particles

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 :

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Linear Momentum of a System of Particles

A mass

M

attached to a horizontal spring executes

S . H . M .

of amplitude

A_{1}

. When the mass

M

passes through its mean position, then a smaller mass

m

is placed over it and both of them move together with amplitude

A_{2}

. The ratio of

(\frac{A_{1}}{A_{2}})

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Linear Momentum of a System of Particles

A ball hits the floor and rebounds after an inelastic collision. In this case

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Linear Momentum of a System of Particles

An object

A

of mass

20 kg

and travelling at

20 m s^{- 1}

crashes into another object

B

of mass

200 kg

and travelling at

10 m s^{- 1},

in the same direction. After the collision, object

A

bounces back in opposite direction at a speed of

10 m s^{- 1}

. The speed of the object

B

after the collision is

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Linear Momentum of a System of Particles

A block moving horizontally on a smooth surface with a speed of

40 {m s}^{- 1}

splits into two equal parts. If one of the parts moves at

60 {m s}^{- 1}

in the same direction, then the fractional change in the kinetic energy will be

x : 4

where

x =

________.

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Linear Momentum of a System of Particles

Given the masses of various atomic particles

m_{P} = 1, 0072 u

m_{n} = 1, 0087 u

m_{e} = 0 .000548 u

m_{\bar{v}} = 0

m_{d} = 2 .0141 u

, where

p =

proton,

n \equiv

neutron,

e \equiv

electron,

\bar{v} \equiv

antineutrino and

\bar{d} \equiv

deuteron. Which of the following process is allowed by momentum and energy conservation :

HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Linear Momentum of a System of Particles

A man (mass

= 50 k g

) and his son (mass

= 20 k g

) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of

0.70 m s^{- 1}

with respect to the man. The speed of the man with respect to the surface is:

HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Linear Momentum of a System of Particles

A particle of mass

m

is projected from the ground with an initial speed

u_{\circ}

at an angle

α

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_{\circ}

. The angle that the composite system makes with the horizontal immediately after the collision is

A flat car of mass M is at rest on a frictionless floor with a child of mass m standing at the edge. If the child jumps off from the car towards right with initial velocity u, with respect to car, find the velocity of car after the jump.

Important Questions on Systems of Particles and Rotational Motion

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A flat car of mass $M$ is at rest on a frictionless floor with a child of mass m standing at the edge. If the child jumps off from the car towards right with initial velocity $u$ , with respect to car, find the velocity of car after the jump.