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 cylinder manufacturer makes small and large cylinders from a large piece of cardboard. The large cylinder requires 4 sq. m and small cylinder requires 3 sq. m of cardboard. The manufacturer is required to make at least 3 large cylinder and at least twice as many small cylinder as large cylinders. If 60 sq. m of cardboard is in the stock and profit on the small and large cylinders are Rs. 25 and Rs 35 respectively. How many of each type of cylinders to made to maximize the profit. Also, find the maximum profit.

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 .

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

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