A uniform rope of lrngth L is pulled by constant force F. What is the tension in the rope at a distance `l` from the end, where it is applied ?

A rope of length L is pulled with a constant force F.The tension T in the rope at u point at distance x from the end where the force is applied ,is :

A beam of length'l' is suported at one end. If W is the uniform load per unit length, the bending moment M at a distance 'x' from the end is given by M =1/2 lx -1/2 Wx^2 Find the point on the beam at which the bending moment has maximum value.

A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N ? What is the linear acceleration of the rope ? Assume that there is no slipping.

A wire of length L and radius r is clalmped rigidly at one end. When the other end of the wire is pulled by force f, its length increaes by l. Another wire of the same material of length 2 L and radius 2 r, is pulled by a force 2 f. Find the increase in length of this wire.

A uniform disc of radius R, is resting on a table on its rim. The coefficent of friction between disc and table is mu (show in the figure). Now the disc is pulled with a force F . What is the maximum value of F for which the disc rolls without slipping?

A metal bar AB can slide on two parallel thick metallic rails separated by a distance l. A resistance R and an inductance L are connected to the rails as shown in the figure. A long straight wire carrying a constant current I_(0) is placed in the plane of the rails and perpendicular to them as shown. The bar AB is held at rest at a distance x_(0) from the long wire. At t=0, it is made to slide on the rails away from wire. Answer the following questions. Find a relation among i, (di)/(dt) and (d phi)/(dt) , where i is the current in the circuit and phi is the flux of the megnetic field due to the long wire through the circuit.

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