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A shell initially at rest explodes into two pieces of equal mass, the two pieces will

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Important Questions on Systems of Particles and Rotational Motion

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Motion of Center of Mass

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?

HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Motion of Center of Mass

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:

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Motion of Center of Mass

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>Motion of Center of Mass

Two masses of

1 g

and

4 g

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

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Motion of Center of Mass

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

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Motion of Center of Mass

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?

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Motion of Center of Mass

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:

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Motion of Center of Mass

If momentum is decreased by

20 %

, kinetic energy will decrease by

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Motion of Center of Mass

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}

]

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Motion of Center of Mass

A ball is thrown vertically up (taken as

+ z - a x i s

) from the ground. The correct momentum-height

(p - h)

diagram is:

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Motion of Center of Mass

A stationary body explodes into two parts of masses

M_{1}

and

M_{2}

. They move in opposite directions with velocities

v_{1}

and

v_{2}

. The ratio of their kinetic energies is

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Motion of Center of Mass

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:

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Motion of Center of Mass

Two bodies of mass

m

and

4 m

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

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Motion of Center of Mass

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

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Motion of Center of Mass

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>Motion of Center of Mass

A ball of mass $10 kg$ moving with a velocity $10 \sqrt{3} m s^{- 1}$ along the $x$ -axis, hits another ball of mass $20 kg$ which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along $y$ -axis with a speed of $10 m s^{- 1} .$ The second piece starts moving at an angle of $30 °$ with respect to the $x$ -axis. The velocity of the ball moving at $30 °$ with $x$ -axis is $x m s^{- 1} .$ The configuration of pieces after the collision is shown in the figure below. The value of $x$ to the nearest integer is

Question Image

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Motion of Center of Mass

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>Motion of Center of Mass

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:

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Motion of Center of Mass

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>Motion of Center of Mass

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 shell initially at rest explodes into two pieces of equal mass, the two pieces will

Important Questions on Systems of Particles and Rotational Motion

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