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 crate of mass m falls from a height $h$ onto the end of a platform, as shown in the figure. The spring is initially unstretched and the mass of the platform can be neglected. What will be the maximum elongation of the spring assuming that there is no loss of energy,

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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

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:

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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

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,

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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

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

A block of mass

1 k g

is free to move along the

X

-axis. It is at rest and from time

t = 0

onwards it is subjected to a time-dependent force

F (t)

in the

x

-direction. The force

F (t)

varies with

t

as shown in figure. The kinetic energy of the block at

t = 4

s 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 :

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

A wedge of mass

M = 4 m

lies on a frictionless plane. A particle of mass

m

approaches the wedge with speed

v .

There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by:

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

A ball of mass

M

moving with a speed of

2 m s^{- 1}

hits another ball of mass

1 kg

moving in the same direction with a speed of

1 m s^{- 1}

. If the kinetic energy of center of mass is

\frac{4}{3} Joule

, then the magnitude of

M

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

In free space, a particle

A

of charge

1 μ C

is held fixed at point

P

. Another particle

B

of the same charge and mass

4 μ g

is kept at a distance of

1 m m

from

P .

B

is released, then its velocity at a distance of

9 m m

from

P

is:
[Take

\frac{1}{4 π ϵ_{0}} = 9 \times 10^{9} N m^{2} C^{- 2}

]

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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:

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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

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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

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 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

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

The escape velocity from the surface of earth is

v_{e} .

A body is projected with velocity

3 v_{e} .

With what constant velocity will it move in the inter planetary space?

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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

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

A bullet of mass

m

moving horizontally with speed

v_{0}

hits a wooden block of mass

M

that is suspended from a massless string. The bullet gets lodged into the block and comes into halt. If the block-bullet combine swings to a maximum height

h

then how much of the initial kinetic energy of the bullet is lost in the collision?

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

A body of mass

(4 m)

is lying in

x

y

plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass

(m)

move perpendicular to each other with equal speeds

(υ) .

The total kinetic energy generated due to explosion is:

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

A bullet of mass

10 g

moving horizontally with a velocity of

400 m s^{- 1}

strikes a wooden block of mass

2 kg

which is suspended by a light inextensible string of length

5 m.

As a result, the centre of gravity of the block is found to rise a vertical distance of

10 cm.

The speed of the bullet after it emerges out horizontally from the block will be

HARD

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

A block of mass

m = 0.1 kg

is connected to a spring of unknown spring constant k. It is compressed to a distance

x

from its equilibrium position and released from rest. After approaching half the distance

(\frac{x}{2})

from the equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with velocity

3 m s^{- 1}

. The total initial energy of the spring is:

A crate of mass m falls from a height $h$ onto the end of a platform, as shown in the figure. The spring is initially unstretched and the mass of the platform can be neglected. What will be the maximum elongation of the spring assuming that there is no loss of energy,

Important Questions on Systems of Particles and Rotational Motion

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