Physics-
General
Easy
Question
Two blocks A and B of equal masses m kg each are connected by a light thread, which passes over a massless pulley as shown in the figure. Both the blocks lie on wedge of mass m kg. Assume friction to be absent everywhere and both the blocks to be always in contact with the wedge. The wedge lying over smooth horizontal surface is pulled towards right with constant acceleration a (
). (g is acceleration due to gravity) Normal reaction (in N) acting on block B is
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/472059/1/944859/Picture121.png)
(3g + 4a)
(3g – 4a)
(4g + 3a)
(4g – 3a)
The correct answer is:
(3g + 4a)
Related Questions to study
physics-
A light inextensible string connects a block of mass m and top of wedge of mass M. The string is parallel to inclined surface and the inclined surface makes an angle
with horizontal as shown in the figure. All surfaces are smooth. Now a constant horizontal force of minimum magnitude F is applied to wedge towards right such that the normal reaction on block exerted by wedge just becomes zero. The magnitude of acceleration of wedge is
![](data:image/png;base64,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)
A light inextensible string connects a block of mass m and top of wedge of mass M. The string is parallel to inclined surface and the inclined surface makes an angle
with horizontal as shown in the figure. All surfaces are smooth. Now a constant horizontal force of minimum magnitude F is applied to wedge towards right such that the normal reaction on block exerted by wedge just becomes zero. The magnitude of acceleration of wedge is
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)
physics-General
maths-
The vector
which is perpendicular to (2,-3,1) and (1,-2,3) and which satisfies the condition ![stack x with minus on top times open parentheses stack i with minus on top plus 2 stack j with minus on top minus 7 k close parentheses equals 10](data:image/png;base64,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)
The vector
which is perpendicular to (2,-3,1) and (1,-2,3) and which satisfies the condition ![stack x with minus on top times open parentheses stack i with minus on top plus 2 stack j with minus on top minus 7 k close parentheses equals 10](data:image/png;base64,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)
maths-General
Maths-
Let f : R → R be a differentiable function satisfying f (x) = f (x – y) f (y) " x, y Î R and f ¢ (0) = a, f ¢ (2) = b then f ¢ (-2) is
Let f : R → R be a differentiable function satisfying f (x) = f (x – y) f (y) " x, y Î R and f ¢ (0) = a, f ¢ (2) = b then f ¢ (-2) is
Maths-General
physics-
Four identical metal butterflies are hanging from a light string of length
at equally placed points as shown in the figure . The ends of the string are attached to a horizontal fixed support. The middle section of the string is horizontal. The relation between the angle
and
is given by
![](data:image/png;base64,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)
Four identical metal butterflies are hanging from a light string of length
at equally placed points as shown in the figure . The ends of the string are attached to a horizontal fixed support. The middle section of the string is horizontal. The relation between the angle
and
is given by
![](data:image/png;base64,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)
physics-General
physics-
Initially the spring is undeformed. Now the force 'F' is applied to 'B' as shown in the figure . When the displacement of 'B' w.r.t 'A' is 'x' towards right in some time then the relative acceleration of 'B' w.r.t. 'A' at that moment is:
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471906/1/944733/Picture147.png)
Initially the spring is undeformed. Now the force 'F' is applied to 'B' as shown in the figure . When the displacement of 'B' w.r.t 'A' is 'x' towards right in some time then the relative acceleration of 'B' w.r.t. 'A' at that moment is:
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471906/1/944733/Picture147.png)
physics-General
physics-
Mass m shown in the figure is in equilibrium. If it is displaced further by x and released find its acceleration just after it is released. Take pulleys to be light & smooth and strings light.
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471932/1/944732/Picture146.png)
Mass m shown in the figure is in equilibrium. If it is displaced further by x and released find its acceleration just after it is released. Take pulleys to be light & smooth and strings light.
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471932/1/944732/Picture146.png)
physics-General
physics-
In the figure shown, the pulleys and strings are massless. The acceleration of the block of mass 4m just after the system is released from rest is ![open parentheses theta equals s i n to the power of negative 1 end exponent invisible function application fraction numerator 3 over denominator 5 end fraction close parentheses](data:image/png;base64,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)
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471896/1/944729/Picture145.png)
In the figure shown, the pulleys and strings are massless. The acceleration of the block of mass 4m just after the system is released from rest is ![open parentheses theta equals s i n to the power of negative 1 end exponent invisible function application fraction numerator 3 over denominator 5 end fraction close parentheses](data:image/png;base64,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)
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471896/1/944729/Picture145.png)
physics-General
maths-
If S and
are two foci of an ellipse
+
= 1
and P
a point on it, then SP +
P is equal to-
If S and
are two foci of an ellipse
+
= 1
and P
a point on it, then SP +
P is equal to-
maths-General
physics-
A cylinder rests in a supporting carriage as shown. The side AB of carriage makes an angle
with the horizontal and side BC is vertical. The carriage lies on a fixed horizontal surface and is being pulled towards left with an horizontal acceleration 'a'. The magnitude of normal reactions exerted by sides AB and BC of carriage on the cylinder be
respectively. Neglect friction everywhere. Then as the magnitude of acceleration 'a ' of the carriage is increased, pick up the correct statement:
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471892/1/944726/Picture144.png)
A cylinder rests in a supporting carriage as shown. The side AB of carriage makes an angle
with the horizontal and side BC is vertical. The carriage lies on a fixed horizontal surface and is being pulled towards left with an horizontal acceleration 'a'. The magnitude of normal reactions exerted by sides AB and BC of carriage on the cylinder be
respectively. Neglect friction everywhere. Then as the magnitude of acceleration 'a ' of the carriage is increased, pick up the correct statement:
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471892/1/944726/Picture144.png)
physics-General
physics-
In the figure shown, a person wants to raise a block lying on the ground to a height h. In both the cases if time required is same then in which case he has to exert more force. Assume pulleys and strings light.
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/471890/1/944724/Picture142.png)
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471890/1/944724/Picture143.png)
In the figure shown, a person wants to raise a block lying on the ground to a height h. In both the cases if time required is same then in which case he has to exert more force. Assume pulleys and strings light.
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/471890/1/944724/Picture142.png)
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471890/1/944724/Picture143.png)
physics-General
physics-
A rod of length
is moving such that its ends A and B move in contact with the horizontal floor and vertical wall respectively as shown in figure. O is the intersection point of the vertical wall and horizontal floor. The velocity vector of the centre of rod C is always directed along tangent drawn at C to the –
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471880/1/944723/Picture141.png)
A rod of length
is moving such that its ends A and B move in contact with the horizontal floor and vertical wall respectively as shown in figure. O is the intersection point of the vertical wall and horizontal floor. The velocity vector of the centre of rod C is always directed along tangent drawn at C to the –
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471880/1/944723/Picture141.png)
physics-General
maths-
The orthogonal projection of
on
are unit vectors along three mutually perpendicular directions )
The orthogonal projection of
on
are unit vectors along three mutually perpendicular directions )
maths-General
maths-
If S and
are foci and A be one and of minor axis of ellipse
+
= 1, then area of
is-
If S and
are foci and A be one and of minor axis of ellipse
+
= 1, then area of
is-
maths-General
maths-
Q is a point on the auxiliary circle corresponding to the point P of the ellipse
= 1. If T is the foot of the perpendicular dropped from the focus S. onto the tangent to the auxiliary circle at Q then the
SPT is -
Q is a point on the auxiliary circle corresponding to the point P of the ellipse
= 1. If T is the foot of the perpendicular dropped from the focus S. onto the tangent to the auxiliary circle at Q then the
SPT is -
maths-General
physics-
A bob is hanging over a pulley inside a car through a string. The second end of the string is in the hand of a person standing in the car. The car is moving with constant acceleration 'a' directed horizontally as shown in figure. Other end of the string is pulled with constant acceleration ' a ' vertically downward. The tension in the string is equal to :
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471835/1/944634/Picture129.png)
A bob is hanging over a pulley inside a car through a string. The second end of the string is in the hand of a person standing in the car. The car is moving with constant acceleration 'a' directed horizontally as shown in figure. Other end of the string is pulled with constant acceleration ' a ' vertically downward. The tension in the string is equal to :
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/471835/1/944634/Picture129.png)
physics-General