Systems of Part...

A horizontal turn table in the form of a disc of radius r carries a gun at G and rotates with angular velocity ω₀ about a vertical axis passing through the centre O. The increase in angular velocity of the system if the gun fires a bullet of mass m with a tangential velocity υ w.r.t the gun is (where I₀ is moment of inertia of gun + table, about O)

A sphere is rotating between two rough inclined walls as shown in Fig. Coefficient of friction between each wall and the sphere is 1/3. If f₁ and f₂ be the frictional forces at P and Q, then f₁/f₂ is

Three particles, each of mass m are placed at the corners of a right angled triangle as shown in Fig. If OA = a and OB = b, the position vector of the centre of mass is

Find the centre of mass of a metal circular sheet of diameter 6 cm, which has a 2 cm square cut out of it. The two sides of the square lie along diameters of the circle. OM is bisector of ∠AOD, Fig.

A uniform bar of length 6 α and mass 8 m lies on a smooth horizontal table. Two point masses m and 2 m moving in the same horizontal plane with speeds 2 v and v resp. strike the bar as shown in fig. and stick to the bar after collision. Denoting angular velocity about the centre of mass, total energy and centre of mass velocity by ω, E and v_c respectively, we have after collision

The centre of mass of a systems of two particles is

Particles of 1 gm, 1 gm, 2 gm, 2 gm are placed at the corners A, B, C, D, respectively of a square of side 6 cm as shown in figure. Find the distance of centre of mass of the system from geometrical centre of square.

From a uniform circular disc of radius R, a circular disc of radius R/6 and having centre at a distance + R/2 from the centre of the disc is removed. Determine the centre of mass of remaining portion of the disc.

A circular plate of uniform thickness has a diameter of 56 cm. A circular portion of diameter 42 cm. is removed from +ve x edge of the plate. Find the position of centre of mass of the remaining portion with respect to centre of mass of whole plate.

A circular disc of radius R is removed from a bigger disc of radius 2R. such that the circumferences of the disc coincide. The centre of mass of the remaining portion is R from the centre of mass of the bigger disc. The value of α is.