A large spherical mass M is fixed at one position and two identical masses m are kept on a line passing through the centre of M (see figure). The point masses are connected by a rigid massless rod of length l and this assembly is free to move along the line connecting them.


All three masses interact only through their mutual gravitational interaction. When the point mass nearer to M is at a distance r = 3l from M the tension in the rod is zero for m = $$k\left( {{M \over {288}}} \right)$$. The value of k is

In plotting stress versus strain curves for two materials P and Q, a student by mistake puts strain on the y-axis and stress on the x-axis as shown in the figure. Then, the correct statements is/are

A parallel plate capacitor having plates of area S and plate separation d, has capacitance C₁ in air. When two dielectrics of different relative permittivities ($$\varepsilon $$₁ = 2 and $$\varepsilon $$₂ = 4) are introduced between the two plates as shown in the figure, the capacitance becomes C₂. The ratio $${{{C_2}} \over {{C_1}}}$$ is

An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston (as shown in the figure). Initially the gas is at temperature T₁, pressure P₁ and volume V₁ and the spring is in its relaxed state. The gas is then heated very slowly to temperature T₂, pressure P₂ and volume V₂. During this process the piston moves out by a distance x.

Ignoring the friction between the piston and the cylinder, the correct statements is/are