Three girls skating on a circular ice ground of radius 200 m start from a point P on the edge of the ground and reach a point Q diametrically opposite to Pfollowing different paths as shown in Fig. 4.20. What is the magnitude of the displacement vector for each ? For which girl is this equal to the actual length of path skate?

A man leaves his home early in the morning to have a walk. He arrives at a junction of roads A and B as shown in figure. He takes the following steps in later journies : (i) 1 km in North direction. (ii) Changes direction and moves in North-East direction for 2 sqrt(2) km. (iii) Changes direction and moves Southwards for distance of 2 km. (iv) Finally he changes the direction and moves in South-East direction to reach road A again. Now if roads A and B are taken as X-axis and y-axis ,then visible point representing the graph of y=f(x) Then the value of x at which function f(x) is discontinous

A man leaves his home early in the morning to have a walk. He arrives at a junction of roads A and B as shown in figure. He takes the following steps in later journies : (i) 1 km in North direction. (ii) Changes direction and moves in North-East direction for 2 sqrt(2) km. (iii) Changes direction and moves Southwards for distance of 2 km. (iv) Finally he changes the direction and moves in South-East direction to reach road A again. Now if roads A and B are taken as X-asix and Y-axis, then visible point representing the graph of y = f(x). Then the value of x at which function f(x) is discontionous

A man leaves his home early in the morning to have a walk. He arrives at a junction of roads A and B as shown in figure. He takes the following steps in later journies : (i) 1 km in North direction. (ii) Changes direction and moves in North-East direction for 2 sqrt(2) km. (iii) Changes direction and moves Southwards for distance of 2 km. (iv) Finally he changes the direction and moves in South-East direction to reach road A again. Now if roads A and B are taken as X-asix and Y-axis, then visible point representing the graph of y = f(x). Then the value of x at which function f(x) is discontionous

A particle P starts from the point z_0=1+2i , where i=sqrt(-1) . It moves first horizontally away from origin by 5 units and then vertically away from origin by 3 units to reach a point z_1dot From z_1 the particle moves sqrt(2) units in the direction of the vector hat i+ hat j and then it moves through an angle pi/2 in anticlockwise direction on a circle with centre at origin, to reach a point z_2dot The point z_2 is given by

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

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 a 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. Equation of the sphere having centre at (3, 6, -4) and touching the plane rcdot(2hat(i)-2hat(j)-hat(k))=10 is (x-3)^2+(y-6)^2+(z+4)^2=k^2 , where k is equal to

A simple pendulum of length 1 and having a bob of mass M is suspended in a car. The car is moving on a circular track of radius R with a uniform speed v. If the pendulum makessmall oscillations in a radial direction about its equilibrium position, what will be its time period ?

Two fixed, equal, positive charges, each of magnitude 5xx10^-5 coul are located at points A and B separated by a distance of 6m. An equal and opposite charge moves towards them along the line COD, the perpendicular bisector of the line AB. The moving charge, when it reaches the point C at a distance of 4m from O, has a kinetic energy of 4 joules. Calculate the distance of the farthest point D which the negative charge will reach before returning towards C.