A particle suspended from a fixed point, by a light inextensible thread of length L is projected horizontally from its lowest position with velocity `(7gL/2)^(1/2)` . The thread will slack after swinging through an angle `theta`, such that `theta` equal

A ball is projected horizontally with a velocity of 4 ms^-1 .What will be its velocity after 0.7 sec (g=10 m s^-2) ?

The stone of mass 100 g is suspended from the end of a weightless string of length 100 cm and is allowed to swing in a vertical plane.The speed of the mass is 2 m s^-1 when the string makes an angle of 60^@ with the vertical .Calculate the tension in the string at theta = 60^@ .Also,caculate the speed of the stone when it is in the lowest poition. (g=9.8 m s^(-2) ) .

Two particles of equal masses m and m are connected by a light string of length 2l. A constant force F is applied continuously at the mid-point of the string, always along the perpendicular bisector of the straight line joining the two particles. Show that when the distance between the two particles is x, the acceleration of the particle is a = F/m = (x)/((1^2 - x^2) ^(1//2)

A charged particle of mass 1 g is suspended through a silk thread of length 40 cm in a horizontal electric field.fo 4.0 xx 10^4NC^-1 . If the particle stays at a distane of 24 cm from the wall in equilirbium, find the charge on the particle.

Two small spheres each having mass m kg and charge q coulomb are suspended from a point by insultaing threads each l metre long but of negligible mass. If theta is the angle, each string makes with the vertical when equilibrium has been attained show that q^2 = (4m g l^2 sin ^2 theta tan theta) 4 pi upsilon_0

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 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

Two pith-balls each of mass 5xx10^-4 kg are suspended from the same point by silk threads 0.2 m long equal charges are given to the balls, which separate, until the threads enclose an angle of 30^@ , Calculate the charge on each pith-ball.

A small cork ball with a mass 0.58 g is suspended from a thread 10 cm long. Another ball is fixed at a distance 10 cm from the point of suspension and at a distance of 5 cm from the thread as shown in the figure What shoud the magnitude of the like and equal charges on the balls be t deflect the thread through 30^@ ?

A coil in the shape of an equilateral triangle of side 0.02 m is suspended from a vertex such that it is hanging in a vertical plane between the pole pieces of a permanent magnet producing a horizontal magnetic field of 5 xx 10^(-2) T. Find the couple acting on the coil when a current of 0.1 A is passed through it and the magnetic field is parallel to its plane.