An astronaut, in a space shuttle, orbiting close to the earth's surface (take \(g= 10~\text{m/s}^2\)), suddenly fires his engines so as to give him a forward acceleration of \(\dfrac{3g}{4}\) along the direction of his motion. At that instant, his apparent weight is:

The mass \(m\) can slide along a smooth radial groove in a horizontal turntable; at the other end is attached a spring- so that the mass \(m\) presses against the spring as it moves 'outward'. The free-end (\(A\)) of the spring is at a distance \(b\) from the centre and the spring constant is \(k.\) If the turntable is rotated with an angular speed \(\omega\), and the mass \(m\) is in 'equilibrium' with the spring compressed, then the compression is: