A binary star consists of two stars A (mass 2.2M_s) and B (mass 11M_s), where M_s is the mass of the sun. They are separated by distance d and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of star B about the centre of mass is

Gravitational acceleration on the surface of a planet is $${{\sqrt 6 } \over {11}}g$$, where $$g$$ is the gravitational acceleration on the surface of the earth. The average mass density of the planet is $${2 \over 3}$$ times that of the earth. If the escape speed on the surface of the earth is taken to be 11 kms^-1, the escape speed on the surface of the planet in kms^-1 will be

A 0.1 kg mass is suspended from a wire of negligible mass. The length of the wire is 1 m and its crosssectional area is 4.9 $$ \times $$ 10^-7 m². If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency 140 rad s⁻¹. If the Young’s modulus of the material of the wire is n $$ \times $$ 10⁹ Nm^-2, the value of n is

A real gas behaves like an ideal gas if its