Cylinder

The axis of the uniform cylinder in figure is fixed. The cylinder is initially at rest. The block of mass M is initially moving to the friction and with speed v_(1) . It passes over the cylinder to the dashed position. When it first makes contact with the cylinder, it slips on the cylinder, but the friciton is large enough so that slipping ceases before M loses contacts wtih the cylinder. the cylinder has a radius R and a rotaitonal intertia I For the entire process the quantitiy (ies) which will remain conserved for the (cylinder+block) system is/ are (anuglar momentum is considered about the cylinder axis)

A small cylinder of2 cm diamete r is connected to a large cylinder of 20 cm di ameter and each cylinder is fitted with suitable pistons. An incompressibl e fluid is fi lled in the cylinders. If a force of 60 N is appl ied to the piston of the small cylinder, then the force exerted on the p iston of the large cylinder will be

As shown in the adjacent figure, a sphere is placed in a cylinder. It touches the top, bottom and the curved surface of the cylinder. If radius of the base of the cylinder is 'r', (i) what is ratio of the radii of the sphere and the cylinder? (ii)what is the ratio of the curved surface area of the cylinder and the surface area of the sphere? (iii) what is the ratio of the volumes of the cylinder and the sphere?

The hollow cylinder of length l and inner and outer radius R_1 and R_2 respectively. Find resistance of cylinder if current flows radially outward in the cylinder. Resistivity of material of cylinder id rho .

A cylinder of mass m is kept on an inclined plane haivng an angle of inclination 30^(@) . Axis of the cylinder makes an angle 30^(@) with the line along the greatest slope. Assuming that cylinder rolls without slipping, the acceleration of the cylinder is

Three spheres of radius 'r' are kept inside a cylinder such that two of the spheres are at bottom touching each other and sides of the cylinder while the third sphere is touching the two bottom spheres and the top of the cylinder.Then the volume of the cylinder is :

The external and the internal radii of a hollow right circular cylinder of height 15 cm are 6.75 cm and 5.25 cm respectively. If it is melted to form a solid cylinder of height half of the orignal cylinder, then the radius of the solid cylinder is-

A solid metallic right cone is melted and some solid right circular cylinders are made. If the radius of base of each cylinder is half the radius of cone and the height of each cylinder is one third the height of the cone, then the number of cylinders formed are.

In Fig, a lead brick rests horizontally on cylinders A and B. The areas of the top faces of the cylinders are related by A_(A)=2.2 A_(B) , the Young's moduli of the cylinders are related by E_(A) = 2.2 E_(B) . The cyclinders had identical lengths before the brick was placed on them. What fraction of the brick's mass is supported (a) by cylinder A and (b) by cylinder B ? The horizontal distances between the center of mass of the brick and the centerlines of the cylinders are d_(A) for cylinder A and d_(B) for cylinder B. (c ) What is the ratio d_(A)//d_(B) ?