Question
As shown in the figure a particle starts its motion from 0 to
. And then it moves from. A to B.
is an are find the Path length
![](data:image/png;base64,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)
- 2r
The correct answer is: ![r open parentheses 1 plus fraction numerator pi over denominator 3 end fraction close parentheses](data:image/png;base64,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)
Related Questions to study
A particle moves from A to P and then it moves from P to B as shown in the figure. Find path length and displacement.
![](data:image/png;base64,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)
A particle moves from A to P and then it moves from P to B as shown in the figure. Find path length and displacement.
![](data:image/png;base64,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)
A particle moves from A to B and then it moves from B to C as shown in figure. Calculate the ratio between path length and displacement.
![](data:image/png;base64,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)
A particle moves from A to B and then it moves from B to C as shown in figure. Calculate the ratio between path length and displacement.
![](data:image/png;base64,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)
As shown in the figure a particle moves from. 0 to A, and then
to B. Find pathlength and displacement.
![](data:image/png;base64,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)
As shown in the figure a particle moves from. 0 to A, and then
to B. Find pathlength and displacement.
![](data:image/png;base64,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)
The vectors
are equal in length and pair wise make equal angles. If
, then ![c with not stretchy bar on top equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABoAAAATCAYAAACORR0GAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAASM53j1gAAAHpJREFUeNpjYICA/1jwKBgFo2CQAx4g7gLip0D8C4jXAbEgLSw5B8StQMwHxGxAXALEPljU/icC4wQdQDyJ1kHGBMSvaRFM6MAUiA+ToJ7soPOCRjzNgTEQ36BX0r4ATXEs0FRXAMTWtLBIFogPAvEfIL4ExMlDsiQAAFy0JoXYQWz7AAAAkHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtb3ZlciBhY2NlbnQ9InRydWUiPjxtaT5jPC9taT48bW8gc3RyZXRjaHk9ImZhbHNlIj4mI3hBRjs8L21vPjwvbW92ZXI+PG1vPj08L21vPjwvbWF0aD6pOx6qAAAAAElFTkSuQmCC)
For such questions, concept of scalar product is important. When we take a dot product of two vectors, we get a scalar value. This is called as scalar product.
The vectors
are equal in length and pair wise make equal angles. If
, then ![c with not stretchy bar on top equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABoAAAATCAYAAACORR0GAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAASM53j1gAAAHpJREFUeNpjYICA/1jwKBgFo2CQAx4g7gLip0D8C4jXAbEgLSw5B8StQMwHxGxAXALEPljU/icC4wQdQDyJ1kHGBMSvaRFM6MAUiA+ToJ7soPOCRjzNgTEQ36BX0r4ATXEs0FRXAMTWtLBIFogPAvEfIL4ExMlDsiQAAFy0JoXYQWz7AAAAkHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtb3ZlciBhY2NlbnQ9InRydWUiPjxtaT5jPC9taT48bW8gc3RyZXRjaHk9ImZhbHNlIj4mI3hBRjs8L21vPjwvbW92ZXI+PG1vPj08L21vPjwvbWF0aD6pOx6qAAAAAElFTkSuQmCC)
For such questions, concept of scalar product is important. When we take a dot product of two vectors, we get a scalar value. This is called as scalar product.
The figure shows elliptical orbit of a planet m about the sun s . the shaded area SCD is twice, the Saded area SAB. If t1 is the time tor the planet to move trom C' and U and t2 is the time to move from A to B then
![](data:image/png;base64,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)
The figure shows elliptical orbit of a planet m about the sun s . the shaded area SCD is twice, the Saded area SAB. If t1 is the time tor the planet to move trom C' and U and t2 is the time to move from A to B then
![](data:image/png;base64,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)
A Particle of mass
is at rest at t=0. The force exerting on it in
-direction is
. Which one of the following graph is of speed ![V left parenthesis t right parenthesis rightwards arrow t](data:image/png;base64,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)
A Particle of mass
is at rest at t=0. The force exerting on it in
-direction is
. Which one of the following graph is of speed ![V left parenthesis t right parenthesis rightwards arrow t](data:image/png;base64,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)
As shown in figure a block of mass
is aftachod with a cart. If the coefficient of static friction between the surface of cart and block is
than what would be accelcration
of cart to prevent the falling of block ?
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)
As shown in figure a block of mass
is aftachod with a cart. If the coefficient of static friction between the surface of cart and block is
than what would be accelcration
of cart to prevent the falling of block ?
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)
If the vectors
and
make an abtuse angle for any
, then
belangs to
If the vectors
and
make an abtuse angle for any
, then
belangs to
A geostationary satellite is orbiting the earth at a height of 5R above that of surface of the earth. R being the radius of the earth. The time period of another satellite in hours at a height of 2R from the surface of earth is hr.
A geostationary satellite is orbiting the earth at a height of 5R above that of surface of the earth. R being the radius of the earth. The time period of another satellite in hours at a height of 2R from the surface of earth is hr.
The most common minerals of phosphorus are
The most common minerals of phosphorus are
The time period T of the moon of planet Mars(Mm) is related to its orbital radius R as (G = Gravitational constant)
The time period T of the moon of planet Mars(Mm) is related to its orbital radius R as (G = Gravitational constant)
A mass of 6 kg is suspended by a rope of lengih 2 m form the ceiling . A force of 50 N in the horizonlal direction is applied at the mid Point P of the rope as shown in figure. what is the angle the rope makes. with the vertical in equilibrium ?
Neglect mass of the rope:
![](data:image/png;base64,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)
A mass of 6 kg is suspended by a rope of lengih 2 m form the ceiling . A force of 50 N in the horizonlal direction is applied at the mid Point P of the rope as shown in figure. what is the angle the rope makes. with the vertical in equilibrium ?
Neglect mass of the rope:
![](data:image/png;base64,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)
Two bodies A and B cach of mass
are fixed together by a massless spring
force
acts on the mass B as shown in figure. At the instant shown, a body A has an accelcration a. what is the acceleration of B?
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)
Two bodies A and B cach of mass
are fixed together by a massless spring
force
acts on the mass B as shown in figure. At the instant shown, a body A has an accelcration a. what is the acceleration of B?
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)
A block of mass m=4 kg is placed over a rough inclined plane as shown in figure, The cocfficient of friction between the block and plane is s=0.6.A force F=10 N is applied on the block of an angle at 30° The contact force between the block and the plane is
![](data:image/png;base64,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)
A block of mass m=4 kg is placed over a rough inclined plane as shown in figure, The cocfficient of friction between the block and plane is s=0.6.A force F=10 N is applied on the block of an angle at 30° The contact force between the block and the plane is
![](data:image/png;base64,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)
If the unit vectors and
are inclined at an angle
such that
, then
lies in the interval
For an interval, square bracket denotes close bracket and parantheses means open bracket. Close bracket means that point is included in the interval. Opem bracket means the point is not included in the interval.
If the unit vectors and
are inclined at an angle
such that
, then
lies in the interval
For an interval, square bracket denotes close bracket and parantheses means open bracket. Close bracket means that point is included in the interval. Opem bracket means the point is not included in the interval.