A uniform semi-circular disc of radius R has a mass M. The distance of the centre of mass from O of the disc on its radius OC dividing the disc symmetrically is

A particle A of mass M is falling freely, from rest, under gravity of earth. At a height h, above ground, it somehow on its own breaks up into two fragments B and C Error in LaTeX '(m_B > m_C)': KaTeX parse error: Expected 'EOF', got '&' at position 6: (m_B &̲gt; m_C). The change in the path of C.M of A and C.M of B and C is

A charged particle having charge q; mass m is under the action of an electric field $E=E_0\widehat{i}E=E\_0\backslash hat\; i$. At some instant of time, its position coordinates are (a, b). What is the magnitude of torque of force on particle due to electric field about origin of co-ordinates at this moment of time?

A particle is moving in x–y plane. The instantaneous position coordinates of particle are (a, b). There are two forces $F_1=2F_0\widehat{i};F_2=F_0\widehat{j}F\_1=2F\_0\backslash hat\; i;F\_2=F\_0\backslash hat\; j$ acting on the particle. The torque of forces on particle about origin of co-ordinates is

A force $F_1=0.5\widehat{j}F\_1=0.5\; \backslash hat\; j$ newton acts at a point having position co-ordinate $r_1=3\widehat{i}r\_1=3\backslash hat\; i$ meter. Another force $F_2=-0.6\widehat{i}F\_2=-0.6\backslash hat\; i$ acts at a point having position vector $r_2=4\widehat{j}r\_2=4\backslash hat\; j$ meter. The net torque of the two forces about origin of co-ordinates is

A uniform wire of length 2L, mass per unit length $\lambda \backslash lambda$ is bent into a circular loop of 2 turns. The M.I of the loop about any tangent in its own plane is

A uniform sphere of mass M; radius R has M.I, I about any diameter as axis. The sphere is recast into a cube. The M.I of cube about an axis through its mid-point parallel to any side of cube is

The radius of gyration of a solid shape of mass M, radius R about some axis is $\sqrt{2}R\backslash sqrt2\; R$. By what distance the axis of rotation be shifted so that radius of gyration becomes 2R?

A uniform cylinder rolls down an rough inclined plane without slipping. Which of the following statements is incorrect?

A hollow sphere of mass M = 6m; radius R is filled with water of mass m. It is rolling without slipping on a rough horizontal surface. The linear velocity of the system is v. The energy of the arrangement is