One end of a horizontal uniform beam of weight W and length L is hinged on a vertical wall at point O and its other end is supported by a light inextensible rope. The other end of the rope is fixed at point Q, at a height L above the hinge at point O. A block of weight $$\alpha$$W is attached at the point P of the beam, as shown in the figure (not to scale). The rope can sustain a maximum tension of (2$$\sqrt 2 $$)W. Which of the following statement(s) is(are) correct?

A particle of mass M = 0.2 kg is initially at rest in the xy-plane at a point (x = $$-$$l, y = $$-$$h), where l = 10 m and h = 1 m. The particle is accelerated at time t = 0 with a constant acceleration a = 10 m/s² along the positive x-direction. Its angular momentum and torque with respect to the origin, in SI units, are represented by $$\overrightarrow L $$ and $$\overrightarrow \tau $$ respectively. $$\widehat i$$, $$\widehat j$$ and $$\widehat k$$ are unit vectors along the positive x, y and z-directions, respectively. If $$\widehat k$$ = $$\widehat i$$ $$\times$$ $$\widehat j$$ then which of the following statement(s) is(are) correct?

A particle of mass m is attached to one end of a mass-less spring of force constant k, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time t = 0 with an initial velocity u₀. When the speed of the particle is 0.5 u₀. It collides elastically with a rigid wall. After this collision,

A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of 2 ms⁻¹. Which of the following statement(s) is (are) correct for the system of these two masses?