A uniform solid right circular cone of base radius `R` is joined to a uniform solid hemisphere of radius `R` and of the same density, as shown. The centre of mass of the composite solid lies at the centre of base of the cone. The height of the cone is
The volume of the largest right circular cone that can be carved out of a solid hemisphere of radius r is given by
A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the cirucmferences of the discs coincide. The centre of mass of the new disc is alpha/R from the center of the bigger disc. The value of alpha is
Find the volume of right circular cone with radius 6 cm and height 7 cm.
An object comprises of a uniform ring of radius R and its uniform chord AB (not necessarily made of the same material) as shown. Which of the following can not be the centre of mass of object
A joker's cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.
From a circular disc of radius R , a triangular portion is cut (see figure). The distance of the centre of mass of the remainder from the centre of the disc is -
Calculate the gravitational potential at the centre of base of a solid hemisphere of mass M , radius R .
A toy is made in the form of hemisphere sumounted by a right cone whose circular base is joined with the plane surface of the hemisphere . The radius of the base of the cone is 7 cm and its volume is 3/2 of the hemisphere . Calculate the height of the cone and the surface area of the toy correct to 2 places of decimal (Take pi= 3 1/7 )
A cylinder and a cone are of same base radius and of same height. Find the ratio of the volume of the cylinder to the volume of the cone.
