IIT JEE 2009 Physics Paper2 Code 1 Solutions

18.    Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. These have masses m, 2m and m, respectively. The object A moves towards B with a speed 9 m/s and makes an elastic collision with it. Thereafter, B makes completely inelastic collision with C. All motions occur on the same straight line. Find the final speed (in m/s) of the object C.

                       

Sol.   4

                        

        After 1^st collision

        mv_A = mv_A'  + 2mv_B'

        -1 = v_B' -v_A' / 0 - v_A = v_B' = 6 m/s

        After 2^nd collision

        2mv_B'  = (2m + m)v_C => v_C = (2/3) v_B' => v_C = 4 m/s

19.    A cylindrical vessel of height 500 mm has an orifice (small hole) at its bottom. The orifice is initially closed and water is filled in it upto height H. Now the top is completely sealed with a cap and the orifice at the bottom is opened. Some water comes out from the orifice and the water level in the vessel becomes steady with height of water column being 200 mm. Find the fall in height (in mm) of water level due to opening of the orifice.

        [Take atmospheric pressure = 1.0 × 10⁵ N/m², density of water = 1000 kg/m³and g = 10 m/s². Neglect any effect of surface tension].

Sol.   6

                  

        Since,

        P = P₀ - ρgh = 98 × 10³ N/m²

        P₀V₀ = PV

        10⁵[A(500 - H)] = 98 × 10³[A(500 - 200)]

        H = 206 mm

        Level fall = 206 - 200 = 6 mm

        Hence, level fall = 6 mm

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