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)

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A space craft of mass M and moving with velocity v suddenly breaks in two pieces of same mass m. After the explosion one of the mass m becomes stationary. What is the velocity of the other part of craft?

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Important Questions on Systems of Particles and Rotational Motion

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

The bodies of mass

2

gram and

4

grams having same kinetics energy having their ratio of linear momentum as

EASY

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

A bullet of mass

50 g

is fired from a rifle of mass

2 kg

and the total kinetic energy produced by the explosion is

2050 J

. Then the kinetic energy of the bullet and the rifle are

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

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

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:

EASY

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

A bomb at rest explodes into

3

parts of same mass. The momentum of two parts is

- 3 p \hat{i}

and

2 p \hat{j}

respectively. The magnitude of momentum of the third part is

EASY

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

The kinetic energy of a body is increased by

300 %

. Its momentum increases by

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:

EASY

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

If momentum is decreased by

20 %

, kinetic energy will decrease by

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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 :

EASY

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

Two particles of masses $m_{1}, m_{2}$ move with initial velocities $u_{1}$ and $u_{2}$ . On collision, one of the particles get excited to higher level, after absorbing energy $ε.$ If final velocities of particles be $v_{1}$ and $v_{2}$ then we must have:

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

Two masses of

1 g

and

4 g

are moving with equal kinetic energy. The ratio of the magnitudes of their linear momentum is

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

A shell of mass

m

is at rest initially. It explodes into three fragments having mass in the ratio

2 : 2 : 1

. If the fragments having equal mass fly off along mutually perpendicular directions with speed

v

, the speed of the third (lighter) fragment is:

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:

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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 :

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 $(take g = 10 m s^{- 2})$

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EASY

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

The momentum of a body increases by

0.1 %

, its kinetic energy increases by (assume that mass does not change)

EASY

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

Two bodies of mass

m

and

4 m

have equal kinetic energy. What is the ratio of their momentum?

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,

A space craft of mass M and moving with velocity v suddenly breaks in two pieces of same mass m. After the explosion one of the mass m becomes stationary. What is the velocity of the other part of craft?

Important Questions on Systems of Particles and Rotational Motion

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