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Can you associate vectors with (a) the l...

Can you associate vectors with (a) the length of a wire bent into a loop , (b) a plane are a , (c ) a sphere ? Explain .

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A vector can be associated with a plane area
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Read each statement below carefully and state with reasons , if it is true of false : (a) The magnitude of a vector is always a scalar , (b) each component of a vector is always a scalar , (c ) the total path length is always equal to the magnitude of the displacement vector of a particle . (d) the average speed of a either greater or equal to the magnitude of average velocity of the particle over the same interval of time , (e ) Three vectors not lying in a plane can never add up to give a null vector .

A uniform wire of length l is bent into the shape of 'V' as shown. The distance of its centre of mass from the vertex A is :-

if rho is the density of the meterial of a wire and sigma is the breaking stress. The greatest length of the wire that can hang freely without breaking is

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A: Two wire A and B having equal cross sections made from the same material. The length of A is twice to the length of B, hence the increase in length of A is twice to the increase in length of B for a given same weight. R: Increase in length of wire proportional to its length for a given same length.

A circle is the locus of a point in a plane such that its distance from a fixed point in the plane is constant. Anologously, a sphere is the locus of a point in space such that its distance from a fixed point in space in constant. The fixed point is called the centre and the constant distance is called the radius of the circle/sphere. In anology with the equation of the circle |z-c|=a , the equation of a sphere of radius is |r-c|=a , where c is the position vector of the centre and r is the position vector of any point on the surface of the sphere. In Cartesian system, the equation of the sphere, with centre at (-g, -f, -h) is x^2+y^2+z^2+2gx+2fy+2hz+c=0 and its radius is sqrt(f^2+g^2+h^2-c) . Q. Radius of the sphere, with (2, -3, 4) and (-5, 6, -7) as xtremities of a diameter, is

A circle is the locus of a point in a plane such that its distance from a fixed point in the plane is constant. Anologously, a sphere is the locus of a point in space such that its distance from a fixed point in space in constant. The fixed point is called the centre and the constant distance is called the radius of the circle/sphere. In anology with the equation of the circle |z-c|=a , the equation of a sphere of radius is |r-c|=a , where c is the position vector of the centre and r is the position vector of any point on the surface of the sphere. In Cartesian system, the equation of the sphere, with centre at (-g, -f, -h) is x^2+y^2+z^2+2gx+2fy+2hz+c=0 and its radius is sqrt(f^2+g^2+h^2-c) . Q. The centre of the sphere (x-4)(x+4)+(y-3)(y+3)+z^2=0 is

How can you as an individual contribute or make a difference to the management of (a) Forests and wildlife, (b) Water resources and (c) Coal and petroleum ?

The x and y-components of vector A are 4 m and 6 m respectively. The x and y-components of vector A + B are 10 m and 9 m respectively. Calculate for the vector B the following: (a) its x and y-components (b) its length (c ) the angle it makes with x-axis.

NCERT GUJARATI-MOTION IN A PLANE-EXCERCISES
  1. A man can swim with a speed of 4.0 km/h in still water . How long doe...

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  2. In a harbour , wind is blowing at the speed of 72 km/h and the flag on...

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  3. The celling of a long hall is 25 m high What is the maximum horizontal...

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  4. A cricketer can throw a ball to a maximum horizontal distance of 100 m...

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  5. A stone tied to the end of astring 80 cm long is whirled in a horizon...

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  6. An aircraft executes a horizontal loop of radius 1.00 km with a steady...

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  7. Read each statement below carefully and state , with reasons , if it i...

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  8. The position of a particle is given by r=3.0hati-2.0t^(2)hatj+4.0...

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  9. A particle starts from the origin at t=0 s with a velocity of 10.0hatj...

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  10. hatiandhatj are unit vectors along x - and y- axis respectively . What...

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  11. For any arbitrary motion in space , which of the following relations a...

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  12. Read each statement below acrefully and state , with reasons and exam...

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  13. An aircraft is flying at a height of 3400 m above the ground . If th...

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  14. A very has magnitude and direction . Does it have a location in space...

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  15. A vector has both magnitude and direaction . Does it mean that anythin...

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  16. Can you associate vectors with (a) the length of a wire bent into a lo...

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  17. A bullet fired at an angle of 30^(@) with the horizontal hits the grou...

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  18. A fighter plane flying horizontally at an altitude of 1.5 km with spe...

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  19. A cyclist is riding with a speed of 27 km /h . As he approaches a circ...

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  20. (a) Show that for a projectile the angle between the velocity and the...

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