Physics-
A body of mass
is moving with a uniform speed
along a circle of radius
, what is the average acceleration in going from
to
?
Physics-General
- None of these
Answer:The correct answer is:
Here, 
Change in velocity is going from
to
= 
Average acceleration 
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physics-
A body of mass
is moving with a uniform speed of
on friction less surface under the influence of two forces
and
. The net power of the system is

A body of mass
is moving with a uniform speed of
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physics-General
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A small roller coaster starts at point A with a speed
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There is no loss of energy. Therefore, the final velocity is the same as the initial velocity.
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Hence, The speed of roller coaster at point D is
A small roller coaster starts at point A with a speed
on a curved track as shown in the figure.
The friction between the roller coaster and the track is negligible and it always remains in contact with the track. The speed of roller coaster at point
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physics-General
There is no loss of energy. Therefore, the final velocity is the same as the initial velocity.
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physics-
A block(B) is attached to two unstretched springs
with springs constants
representively (see Fig. I) The other ends are attached to identical supports
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The ratio
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From energy conservation,


A block(B) is attached to two unstretched springs
with springs constants
representively (see Fig. I) The other ends are attached to identical supports
and
not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block
is displaced towards wall I by small distance
and released. The block returns and moves a maximum distance y towards wall 2.Displacements
are measured with respect to the equilibrium position of the block
The ratio
is

physics-General
From energy conservation,


physics-
In a two dimensional motion of a particle, the particle moves from point
, position vector
. If the magnitudes of these vectors are respectively,
=3 and
and the angles they make with the
-axis are
and 15
, respectively, then find the magnitude of the displacement vector

Displacement 
angle between
and 

From figure

cos


angle between
From figure
In a two dimensional motion of a particle, the particle moves from point
, position vector
. If the magnitudes of these vectors are respectively,
=3 and
and the angles they make with the
-axis are
and 15
, respectively, then find the magnitude of the displacement vector

physics-General
Displacement 
angle between
and 

From figure

cos


angle between
From figure
physics-
A point
moves in counter-clockwise direction on a circular path as shown in the figure. The movement of
is such that it sweeps out a length
, where
is in metres and
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. The acceleration of
when
is nearly

As 


at




at
A point
moves in counter-clockwise direction on a circular path as shown in the figure. The movement of
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. The acceleration of
when
is nearly

physics-General
As 


at




at
maths-
The area of an ellipse is 8π sq. units dist. between the foci is
then e=
The area of an ellipse is 8π sq. units dist. between the foci is
then e=
maths-General
physics-
From an inclined plane two particles are projected with same speed at same angle
, one up and other down the plane as shown in figure, which of the following statements is/are correct?


So,
From an inclined plane two particles are projected with same speed at same angle
, one up and other down the plane as shown in figure, which of the following statements is/are correct?

physics-General

So,
physics-
A particle is projected from a point
with velocity
at an angle of
with horizontal as shown in figure. It strikes the plane
at right angles. The velocity of the particle at the time of collision is

Let
be the velocity at the time of collision

Then,


Then,
A particle is projected from a point
with velocity
at an angle of
with horizontal as shown in figure. It strikes the plane
at right angles. The velocity of the particle at the time of collision is

physics-General
Let
be the velocity at the time of collision

Then,


Then,
maths-
If the chords of contact of
and
w.r.t the ellipse
are at right angle then 
If the chords of contact of
and
w.r.t the ellipse
are at right angle then 
maths-General
physics-
A particle of a mass
is subjected to a force which varies with distance as shown in fig. If it starts its journey from rest at
, its velocity at
is

Area between curve and displacement axis

In this time body acquire kinetic energy
By the law of conservation of energy


In this time body acquire kinetic energy
By the law of conservation of energy
A particle of a mass
is subjected to a force which varies with distance as shown in fig. If it starts its journey from rest at
, its velocity at
is

physics-General
Area between curve and displacement axis

In this time body acquire kinetic energy
By the law of conservation of energy


In this time body acquire kinetic energy
By the law of conservation of energy
physics-
A particle
is sliding down a frictionless hemispherical bowl. It passes the point
at
. At this instant of time, the horizontal component of its velocity
. A bead
of the same mass as
is ejected from
to
along the horizontal string
(see figure) with the speed
. Friction between the bead and the string may be neglected. Let
and
be the respective time taken by
and
to reach the point
. Then
For particle
, motion between
and
will be an accelerated one while between
and
a retarded one. But in any case horizontal component of it’s velocity will be greater than or equal to
on the other hand in case of particle
, it is always equal to
. Horizontal displacement of both the particles are equal, so 
A particle
is sliding down a frictionless hemispherical bowl. It passes the point
at
. At this instant of time, the horizontal component of its velocity
. A bead
of the same mass as
is ejected from
to
along the horizontal string
(see figure) with the speed
. Friction between the bead and the string may be neglected. Let
and
be the respective time taken by
and
to reach the point
. Then
physics-General
For particle
, motion between
and
will be an accelerated one while between
and
a retarded one. But in any case horizontal component of it’s velocity will be greater than or equal to
on the other hand in case of particle
, it is always equal to
. Horizontal displacement of both the particles are equal, so 
physics-
A ball of mass
rests on a vertical post of height
. A bullet of mass
, travelling with a velocity
in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of
and the bullet at a distance of
from the foot of the post. The initial velocity
of the bullet is

Applying momentum conservation just before and just after the collision
A ball of mass
rests on a vertical post of height
. A bullet of mass
, travelling with a velocity
in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of
and the bullet at a distance of
from the foot of the post. The initial velocity
of the bullet is

physics-General
Applying momentum conservation just before and just after the collision
maths-
P(θ) and
are the pts. on the ellipse
then 
P(θ) and
are the pts. on the ellipse
then 
maths-General
physics-
A simple pendulum is released from
as shown. If
and
represent the mass of the bob and length of the pendulum, the gain in kinetic energy at
is

Vertical height 
Loss of potential energy


Kinetic energy gained 
Loss of potential energy

A simple pendulum is released from
as shown. If
and
represent the mass of the bob and length of the pendulum, the gain in kinetic energy at
is

physics-General
Vertical height 
Loss of potential energy


Kinetic energy gained 
Loss of potential energy

physics-
A particle of mass
attracted with a string of length
is just revolving on the vertical circle without slacking of the string. If
and
are speed at position
and
then

At 
At
and at
Thus,
Also,
So,

At
and at
Thus,
Also,
So,
A particle of mass
attracted with a string of length
is just revolving on the vertical circle without slacking of the string. If
and
are speed at position
and
then

physics-General
At 
At
and at
Thus,
Also,
So,

At
and at
Thus,
Also,
So,