A body of mass m₁ moving with an unknown velocity of $${v_1}\mathop i\limits^ \wedge $$, undergoes a collinear collision with a body of mass m₂ moving with a velocity $${v_2}\mathop i\limits^ \wedge $$ . After collision, m₁ and m₂ move with velocities of $${v_3}\mathop i\limits^ \wedge $$ and $${v_4}\mathop i\limits^ \wedge $$ , respectively. If m₂ = 0.5 m₁ and v₃ = 0.5 v₁, then v₁ is :-

A uniform rectangular thin sheet ABCD of mass M has length a and breadth b, as shown in the figure. If the shaded portion HBGO is cut-off, the coordinates of the centre of mass of the remaining portion will be :-

Four particles A, B, C and D with masses m_A = m, m_B = 2m, m_C = 3m and m_D = 4m are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is :

If 10²² gas molecules each of mass 10^–26 kg collide with a surface (perpendicular to it) elastically per second over an area 1 m² with a speed 10⁴ m/s, the pressure exerted by the gas molecules will be of the order of :