Maths-
If
then descending order of 
is
Maths-General
Answer:The correct answer is: 
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physics-
Three rods of the same mass are placed as shown in figure. What will be the coordinates of centre of mass of the system?

As shown in figure, centre of mass of respective rods are at their respective mid points. Hence centre of mass of the system has coordinates (
,
). then




Three rods of the same mass are placed as shown in figure. What will be the coordinates of centre of mass of the system?

physics-General
As shown in figure, centre of mass of respective rods are at their respective mid points. Hence centre of mass of the system has coordinates (
,
). then




physics-
Two blocks
and
are connected by a massless string (shown in figure). A force of 30 N is applied on block
. The distance travelled by centre of mass in 2 s starting from rest is

The acceleration of centre of mass is


m
Two blocks
and
are connected by a massless string (shown in figure). A force of 30 N is applied on block
. The distance travelled by centre of mass in 2 s starting from rest is

physics-General
The acceleration of centre of mass is


m
physics-
A disc is rolling (without slipping) on a horizontal surface
is its centre and
and
are two points equidistant from
. Let
,
and
be the magnitude of velocities of pints
and
respectively, then

In case of pure rolling bottommost point is the instantaneous centre of zero velocity.

Velocity of any point on the disc,
,
where
is distance of point from
.



Velocity of any point on the disc,
where
A disc is rolling (without slipping) on a horizontal surface
is its centre and
and
are two points equidistant from
. Let
,
and
be the magnitude of velocities of pints
and
respectively, then

physics-General
In case of pure rolling bottommost point is the instantaneous centre of zero velocity.

Velocity of any point on the disc,
,
where
is distance of point from
.



Velocity of any point on the disc,
where
physics-
Find the velocity of centre of the system shown in the figure.

Here,
kg, 
kg, 



Find the velocity of centre of the system shown in the figure.

physics-General
Here,
kg, 
kg, 



physics-
The blocks
and
, each of mass
, are connected by massless spring of natural length
and spring constant
. The blocks are initially resting on a smooth horizontal floor with the spring at its natural length, as shown in figure. A third identical block
, also of mass
, moves on the floor with a speed
along the line joining
and
, and collides with
. Then

The compression of spring is maximum when velocities of both blocks
and
is same. Let it be
, then from conservation law of momentum

kinetic energy of
system at that stage

Further loss in KE> = gain in elastic potential energy
, 

Further loss in KE> = gain in elastic potential energy
The blocks
and
, each of mass
, are connected by massless spring of natural length
and spring constant
. The blocks are initially resting on a smooth horizontal floor with the spring at its natural length, as shown in figure. A third identical block
, also of mass
, moves on the floor with a speed
along the line joining
and
, and collides with
. Then

physics-General
The compression of spring is maximum when velocities of both blocks
and
is same. Let it be
, then from conservation law of momentum

kinetic energy of
system at that stage

Further loss in KE> = gain in elastic potential energy
, 

Further loss in KE> = gain in elastic potential energy
physics-
A set of
identical cubical blocks lies at rest parallel to each other along a line on a smooth horizontal surface. The separation between the near surfaces of any two adjacent blocks is
. The block at one end is given a speed
towards the next one at time
. All collision are completely elastic. Then

Time taken by first block to reach second block 
Since collision is 100% elastic, now first block comes to rest and 2nd block starts moving towards the 3rd block with a velocity
and takes time
to reach 3rd block and so on
Total time
time 
Finally only the last
th block is in motion velocity
, hence final velocity of centre of mass

Since collision is 100% elastic, now first block comes to rest and 2nd block starts moving towards the 3rd block with a velocity
Finally only the last
A set of
identical cubical blocks lies at rest parallel to each other along a line on a smooth horizontal surface. The separation between the near surfaces of any two adjacent blocks is
. The block at one end is given a speed
towards the next one at time
. All collision are completely elastic. Then

physics-General
Time taken by first block to reach second block 
Since collision is 100% elastic, now first block comes to rest and 2nd block starts moving towards the 3rd block with a velocity
and takes time
to reach 3rd block and so on
Total time
time 
Finally only the last
th block is in motion velocity
, hence final velocity of centre of mass

Since collision is 100% elastic, now first block comes to rest and 2nd block starts moving towards the 3rd block with a velocity
Finally only the last
chemistry-
Which of the following noble gas was reacted with
by Bartlett to prepare the first noble gas compounds -
Which of the following noble gas was reacted with
by Bartlett to prepare the first noble gas compounds -
chemistry-General
physics-
In the given figure, two bodies of mass
and
are connected by massless spring of force constant
and are placed on a smooth surface (shown in figure), then

The resultant force on the system is zero. So, the centre of mass of system has no acceleration
In the given figure, two bodies of mass
and
are connected by massless spring of force constant
and are placed on a smooth surface (shown in figure), then

physics-General
The resultant force on the system is zero. So, the centre of mass of system has no acceleration
physics-
Two blocks
and
(
) are connected with a spring of force constant
and are inclined at a angel
with horizontal. If the system is released from rest, which one of the following statements is/are correct?

If the surface is smooth, then relative acceleration between blocks is zero. So, no compression or elongation takes place in spring. Hence, spring force on blocks is zero.
Two blocks
and
(
) are connected with a spring of force constant
and are inclined at a angel
with horizontal. If the system is released from rest, which one of the following statements is/are correct?

physics-General
If the surface is smooth, then relative acceleration between blocks is zero. So, no compression or elongation takes place in spring. Hence, spring force on blocks is zero.
biology
Famous palaeonotologist/Palaeobotanist of India was:
Famous palaeonotologist/Palaeobotanist of India was:
biologyGeneral
physics-
Two negatively charges particles having charges
and
and masses
and
respectively are projected one after another into a region with equal initial velocity. The electric field
is along the
-axis, while the direction of projection makes an angle a with the
-axis. If the ranges of the two particles along the
-axis are equal then one can conclude that

Here, effected gravitational acceleration is


It means,
for both particles are same
This is possible when
and 
It means,
This is possible when
Two negatively charges particles having charges
and
and masses
and
respectively are projected one after another into a region with equal initial velocity. The electric field
is along the
-axis, while the direction of projection makes an angle a with the
-axis. If the ranges of the two particles along the
-axis are equal then one can conclude that

physics-General
Here, effected gravitational acceleration is


It means,
for both particles are same
This is possible when
and 
It means,
This is possible when
physics-
In the given figure four identical spheres of equal mass are suspended by wires of equal length
, so that all spheres are almost touching to each other. If the sphere 1 is released from the horizontal position and all collisions are elastic, the velocity of sphere 4 just after collision is
When the sphere 1 is released from horizontal position, then from energy conservation, potential energy at height
kinetic energy at bottom
Or
Or
Since, all collisions are elastic, so velocity of sphere 1 is transferred to sphere 2, then from 2 to 3 and finally from 3 to 4. Hence, just after collision, the sphere 4 attains a velocity equal to
Or
Or
Since, all collisions are elastic, so velocity of sphere 1 is transferred to sphere 2, then from 2 to 3 and finally from 3 to 4. Hence, just after collision, the sphere 4 attains a velocity equal to
In the given figure four identical spheres of equal mass are suspended by wires of equal length
, so that all spheres are almost touching to each other. If the sphere 1 is released from the horizontal position and all collisions are elastic, the velocity of sphere 4 just after collision is
physics-General
When the sphere 1 is released from horizontal position, then from energy conservation, potential energy at height
kinetic energy at bottom
Or
Or
Since, all collisions are elastic, so velocity of sphere 1 is transferred to sphere 2, then from 2 to 3 and finally from 3 to 4. Hence, just after collision, the sphere 4 attains a velocity equal to
Or
Or
Since, all collisions are elastic, so velocity of sphere 1 is transferred to sphere 2, then from 2 to 3 and finally from 3 to 4. Hence, just after collision, the sphere 4 attains a velocity equal to
physics-
A small object of uniform density roll up a curved surface with an initial velocity
. If reaches up to a maximum height of
with respect to the initial position. The object is

A small object of uniform density roll up a curved surface with an initial velocity
. If reaches up to a maximum height of
with respect to the initial position. The object is

physics-General
physics-
Two identical masses
and
are hanging stationary by a light pulley (shown in the figure). A shell
moving upwards with velocity
collides with the block
and gets stick to it. Then

When
collides with
then due to impulsive force, combined mass (
) starts to move upward. Consequently the string becomes slack
Two identical masses
and
are hanging stationary by a light pulley (shown in the figure). A shell
moving upwards with velocity
collides with the block
and gets stick to it. Then

physics-General
When
collides with
then due to impulsive force, combined mass (
) starts to move upward. Consequently the string becomes slack
physics-
A uniform rod
of length
and mass
is free to rotate about point
. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about
is
, the initial angular acceleration of the rod will be

The moment of inertia of the uniform rod about an axis through one end and perpendicular to its length is

Where
is mass of rod and
is length.
Torque
acting on centre of gravity of rod is given by

or
or
or
Where
Torque
or
or
or
A uniform rod
of length
and mass
is free to rotate about point
. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about
is
, the initial angular acceleration of the rod will be

physics-General
The moment of inertia of the uniform rod about an axis through one end and perpendicular to its length is

Where
is mass of rod and
is length.
Torque
acting on centre of gravity of rod is given by

or
or
or
Where
Torque
or
or
or