A particle is executing simple harmonic motion (SHM) of amplitude A, along the x-axis, about x = 0. When its potential Energy (PE) equals kinetic energy (KE), the position of the particle will be :

A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point. the rope deviated at an angle of 45^o at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is (g = 10 ms^$$-$$2

A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature 27^oC. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about : [Take R = 8.3 J/K mole]

In a Young's double slit experiment, the slits are placed 0.320 mm apart. Light of wavelength $$\lambda $$ = 500 nm is incident on the slits. The total number of bright fringes that are observed in the angular range $$-$$ 30^o$$ \le $$$$\theta $$$$ \le $$30^o is :