Physics-
General
Easy
Question
A particle is acted upon by a force
which varies with position
as shown in the figure. If the particle at
has kinetic energy of 25 J, then the kinetic energy of the particle at
is
![](data:image/png;base64,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)
The correct answer is: ![45 blank J](data:image/png;base64,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)
Work done
Area under
-
graph with proper sign
Area of triangle
+ Area of rectangle
+ Area of rectangle
+ Area of ![I J K L](data:image/png;base64,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)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/904334/1/923520/Picture714.png)
![W equals open square brackets fraction numerator 1 over denominator 2 end fraction blank cross times 6 cross times 10 close square brackets plus open square brackets 4 cross times left parenthesis negative 5 right parenthesis close square brackets plus open square brackets 4 cross times 5 close square brackets plus open square brackets 2 cross times open parentheses negative 5 close parentheses close square brackets](data:image/png;base64,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)
….(i)
According to work energy theorem
![K subscript f end subscript minus K subscript i end subscript equals W rightwards double arrow open parentheses K subscript f end subscript close parentheses subscript x equals 16 m end subscript minus open parentheses K subscript i end subscript close parentheses subscript x equals 0 m end subscript equals W](data:image/png;base64,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)
![open parentheses K subscript f end subscript close parentheses subscript x equals 16 m end subscript equals open parentheses K subscript i end subscript close parentheses subscript x equals 0 m end subscript plus W](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMIAAAAXCAYAAABZEpCtAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAPUJuPDwAABIdJREFUeNrtW11kXEEUHitWHiJEVFRFXioiYoWqiooqVSvyECGqYkWViIqoKtWH6kOViOpDVKlVFVUhoipWlaqIqCoV0YeIJSr6UBHy0IeqFdJzuucmk8nM3L/Zu3f3zschM3fv2Zsz93znZ2YZs4gDnoOMhtSRA3lmTWkGt0CmDeiZJl0W3pwgZ0hXjvRZhEAG5ItBfZ9Jp4UagyALhnUukl6LEC9ur+LaH5CUMHceZA6kSXHPOZBVa1Yt1kG6NNeD2L2L9CYZRZBWYQ7tWFDYq+gMeskRZDgL8l2Y6wd57OGBVskhLE4CX+gVzfUwdl8h/UnFEshlSdr4W/JZrKvuOIMZkEmF0iGQN0I4H/f4QFOGao56xAOQ+5rrYeyOeh/Wmb0OfHx2QZIerpEj8BEWo+ouH10/ENvIgAa9xy1G1scD9YF8su+8FG9BBjTXw9h9gPQn1RFegowIkfQjyHuQHm7+NshT/kb0lLTGu4ZI/Ba/aUU4qrcFchMZfoC0ubBaULufJv1JdQSMtmPcuECp0rwQKTYpBT3EvkvhMQtyNeA/ULLk77kQNmX3FOlPqiPkuJS8k2se5NlRqzpLmRDz4giOQQeIYVo8PESjdYTQCxvE7vVGQEEjLWKY0iOnGB7jatYZrhy4JN6oSo0ucJ2Nu0zefuLDMXreIpd32dRIvWC6hfRj96REYj8RIUuNBmyhbnGR9xrIa4oSG7IbsZC4KJm/zso9awdzmm7EC5Cbtlg2khr5sTtfVNvUqAzM+99JbIP1wRIRtfTkg6p9ijnqBDduYOW9AVkHAwuPM8LcJBeKLLwXy37sLkNbwotlzETWyAb8xmM3yB7IT0kK/x+qDTVZi+8UpUDt3NxXLg3gN3yi3FDrpG7Buku68ddDjhkFdO1Tr3Z3CEicS3r71Kl7pyUOcsBc9rbwnJHYpttTeE4PvVSN3Eu2LHwm6iMWmPuNKwzWTQzRE6OF1W2oebW7KgWKckNtkJxxk8XrjNOeJENhRIQduhvDHLrDnPaVMKc6dLfKzaeoeu/wWYT6ZQ7Msftd7sOFHCWHKVEO2UY1Du4+3jC8UCaIQkZAUUbiPnLMVpJlmqt5TLBgRyJm2fHt/xmmPg6ArDFPf2PRMhxBCN2ll3yblfvzI5LiEkPpN1Y+hJWhz85RypUhhjGNNaY/dBeEgFSH7ipBQFiQ8i3IfipGq0kwsc13ZcCFwu3tfES55D59VzPliXlhAZBZt9jRiUXZeLkCz3pF8uKEISDG5AfOKkVA4tmdFDveLq8WwVQ1H2v0uYCbTH2sw3RqVGQnD1tta5jVbWwST5j3w3RuBDRO+qIiIJmtSzEgmKoAdz13fLIgMtMGdUKiiAh5dnx3Nk0spWJWt7FpoP5cSALy8lNN0wQkRoQGISJUk2AiBb7Uv4hlvKCdiqsmyhUfReQIGQrHzbRY+MJkNczqNq7VtTJNQGKNgH8XYkQwsUSaCrZObrzF1L+0CuIAOgYbpe/bkRTLYmrnNq41VIqA+ii1aSHnWvFJKPVAMBaWgA6L8CKRxVStEsw/NktwYI2NtukAAAFodEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdWI+PG1mZW5jZWQgc2VwYXJhdG9ycz0ifCI+PG1zdWI+PG1pPks8L21pPjxtaT5mPC9taT48L21zdWI+PC9tZmVuY2VkPjxtcm93PjxtaT54PC9taT48bW8+PTwvbW8+PG1uPjE2PC9tbj48bWk+bTwvbWk+PC9tcm93PjwvbXN1Yj48bW8+PTwvbW8+PG1zdWI+PG1mZW5jZWQgc2VwYXJhdG9ycz0ifCI+PG1zdWI+PG1pPks8L21pPjxtaT5pPC9taT48L21zdWI+PC9tZmVuY2VkPjxtcm93PjxtaT54PC9taT48bW8+PTwvbW8+PG1uPjA8L21uPjxtaT5tPC9taT48L21yb3c+PC9tc3ViPjxtbz4rPC9tbz48bWk+VzwvbWk+PC9tYXRoPi+P9/gAAAAASUVORK5CYII=)
[Using (i)]
Related Questions to study
physics-
A bob of mass
accelerates uniformly from rest to
in time
. As a function of
, the instantaneous power delivered to the body is
![](data:image/png;base64,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)
A bob of mass
accelerates uniformly from rest to
in time
. As a function of
, the instantaneous power delivered to the body is
![](data:image/png;base64,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)
physics-General
physics-
An aeroplane is flying in a horizontal direction with a velocity
at a height of 1960 m. when it is vertically above the point
on the ground, a body is dropped from it. The body strikes the ground at point
. Calculate the distance ![A B](data:image/png;base64,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)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486223/1/923498/Picture17.png)
An aeroplane is flying in a horizontal direction with a velocity
at a height of 1960 m. when it is vertically above the point
on the ground, a body is dropped from it. The body strikes the ground at point
. Calculate the distance ![A B](data:image/png;base64,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)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486223/1/923498/Picture17.png)
physics-General
Maths-
If the equation
represents an ellipse then
If the equation
represents an ellipse then
Maths-General
physics-
A particle of mass m moving with horizontal speed
as shown in figure. If
than for one dimensional elastic collision, the speed of lighter particle after collision will be
![](data:image/png;base64,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)
A particle of mass m moving with horizontal speed
as shown in figure. If
than for one dimensional elastic collision, the speed of lighter particle after collision will be
![](data:image/png;base64,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)
physics-General
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
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/904329/1/923462/Picture16.png)
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
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/904329/1/923462/Picture16.png)
Physics-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
![](data:image/png;base64,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)
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
![](data:image/png;base64,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)
physics-General
Maths-
P(θ) and
are the pts. on the ellipse
then ![C P to the power of 2 end exponent plus C D to the power of 2 end exponent equals](data:image/png;base64,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)
P(θ) and
are the pts. on the ellipse
then ![C P to the power of 2 end exponent plus C D to the power of 2 end exponent equals](data:image/png;base64,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)
Maths-General
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
![](data:image/png;base64,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)
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
![](data:image/png;base64,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)
physics-General
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![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486207/1/923382/Picture15.png)
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![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486207/1/923382/Picture15.png)
physics-General
Maths-
If the chords of contact of
and
w.r.t the ellipse
are at right angle then ![fraction numerator x subscript 1 end subscript x subscript 2 end subscript over denominator y subscript 1 end subscript y subscript 2 end subscript end fraction equals](data:image/png;base64,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)
If the chords of contact of
and
w.r.t the ellipse
are at right angle then ![fraction numerator x subscript 1 end subscript x subscript 2 end subscript over denominator y subscript 1 end subscript y subscript 2 end subscript end fraction equals](data:image/png;base64,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)
Maths-General
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-
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
is in seconds. The radius of the path is
. The acceleration of
when
is nearly
![](data:image/png;base64,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)
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
is in seconds. The radius of the path is
. The acceleration of
when
is nearly
![](data:image/png;base64,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)
Physics-General
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
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486202/1/923334/Picture13.png)
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
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486202/1/923334/Picture13.png)
physics-General
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
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
![](data:image/png;base64,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)
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
![](data:image/png;base64,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)
physics-General
physics-
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
on the track will be
![](data:image/png;base64,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)
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
on the track will be
![](data:image/png;base64,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)
physics-General