Physics-
General
Easy
Question
Same spring is attached with 2kg, 3kg and 1 kg blocks in three different cases as shown in figure. If
and
be the extensions in the spring in these three cases then
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471635/1/944351/Picture69.png)
The correct answer is: ![x subscript 2 end subscript greater than x subscript 1 end subscript greater than x subscript 3 end subscript](data:image/png;base64,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)
Related Questions to study
physics-
If masses are released from the position shown in figure then time elapsed before mass m1 collides with the floor will be :
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471592/1/944349/Picture67.png)
If masses are released from the position shown in figure then time elapsed before mass m1 collides with the floor will be :
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471592/1/944349/Picture67.png)
physics-General
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A block A of mass m is placed over a plank B of mass 2m. Plank B is placed over a smooth horizontal surface. The coefficient of friction between A and B is 0.5. Block A is given a velocity v0 towards right. Acceleration of B relative to A is
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471592/1/944349/Picture67.png)
A block A of mass m is placed over a plank B of mass 2m. Plank B is placed over a smooth horizontal surface. The coefficient of friction between A and B is 0.5. Block A is given a velocity v0 towards right. Acceleration of B relative to A is
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471592/1/944349/Picture67.png)
physics-General
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In figure shown, both blocks are released from rest. The time to cross each other ![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471587/1/944348/Picture66.png)
In figure shown, both blocks are released from rest. The time to cross each other ![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471587/1/944348/Picture66.png)
physics-General
physics-
A block A is placed over a long rough plank B of same mass as shown in figure. The plank is placed over a smooth horizontal surface. At time t=0, block A is given a velocity v0 in horizontal direction. Let
and
be the velocities of A and B at time t. Then choose the correct graph between
or
and t
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471624/1/944346/Picture59.png)
A block A is placed over a long rough plank B of same mass as shown in figure. The plank is placed over a smooth horizontal surface. At time t=0, block A is given a velocity v0 in horizontal direction. Let
and
be the velocities of A and B at time t. Then choose the correct graph between
or
and t
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471624/1/944346/Picture59.png)
physics-General
physics-
Three blocks A , B and C of equal mass m are placed one over the other on a smooth horizontal ground as shown in figure. Coefficient of friction between any two blocks of A,B and C is
The maximum value of mass of block D so that the blocks A, B and C move without slipping over each other is
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471592/1/944349/Picture67.png)
Three blocks A , B and C of equal mass m are placed one over the other on a smooth horizontal ground as shown in figure. Coefficient of friction between any two blocks of A,B and C is
The maximum value of mass of block D so that the blocks A, B and C move without slipping over each other is
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471592/1/944349/Picture67.png)
physics-General
physics-
For the system shown in the figure, the acceleration of the mass m4 immediately after the lower thread x is cut will be, (assume that the threads are weightless and inextensible, the spring are weightless, the mass of pulley is negligible and there is no friction)
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471592/1/944349/Picture67.png)
For the system shown in the figure, the acceleration of the mass m4 immediately after the lower thread x is cut will be, (assume that the threads are weightless and inextensible, the spring are weightless, the mass of pulley is negligible and there is no friction)
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471592/1/944349/Picture67.png)
physics-General
physics-
Given
. The coefficient of friction between A and B
= 0.3, between B and C
= 0.2 and between C, and ground,
= 0.1. The least horizontal force F to start motion of any part of the system of three blocks resting upon one another as shown in figure is ( g = 10
)
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471632/1/944343/Picture56.png)
Given
. The coefficient of friction between A and B
= 0.3, between B and C
= 0.2 and between C, and ground,
= 0.1. The least horizontal force F to start motion of any part of the system of three blocks resting upon one another as shown in figure is ( g = 10
)
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471632/1/944343/Picture56.png)
physics-General
maths-
maths-General
maths-
is equal to:
is equal to:
maths-General
maths-
If the chord through the points whose eccentric angles are
and
on the ellipse
=1 passes through the focus (ae, 0), then the value of tan
tan
= 0 is –
If the chord through the points whose eccentric angles are
and
on the ellipse
=1 passes through the focus (ae, 0), then the value of tan
tan
= 0 is –
maths-General
physics-
For a certain mass of a gas Isothermal relation between ‘P’ and ‘V’ are shown by the graphs at two different temperatures T1 and T2 then
![](data:image/png;base64,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)
For a certain mass of a gas Isothermal relation between ‘P’ and ‘V’ are shown by the graphs at two different temperatures T1 and T2 then
![](data:image/png;base64,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)
physics-General
maths-
maths-General
maths-
If the chord joining two points whose eccentric angles are
and
cuts the major axis of an ellipse
+
= 1 at a distance c from the centre, then tan
. tan
is equal to
If the chord joining two points whose eccentric angles are
and
cuts the major axis of an ellipse
+
= 1 at a distance c from the centre, then tan
. tan
is equal to
maths-General
maths-
P(a cos
, b sin
) is any point on the ellipse
+
= 1
Now if this ellipse is rotated anticlockwise by 90º and P reaches
then co-ordinate of
are -
P(a cos
, b sin
) is any point on the ellipse
+
= 1
Now if this ellipse is rotated anticlockwise by 90º and P reaches
then co-ordinate of
are -
maths-General
maths-
Normal to the ellipse
intersects the major and minor axis at P and Q respectively then locus of the point dividing segment PQ in 2 : 1 is -
Normal to the ellipse
intersects the major and minor axis at P and Q respectively then locus of the point dividing segment PQ in 2 : 1 is -
maths-General