A cart is moving along x direction with a velocity of 4 m/s. A person on the cart throws a stone with a velocity of 6 m/s relative to himself. In the frame of reference of the cart the stone is thrown in y-z plane making an angle of 30° with vertical z axis. At the highest point of its trajectory the stone hits an object of equal mass hung vertically from branch of a tree by means of a string of length L.A completely inelastic collision occurs in which the stone gets embedded in the object.
Determine :
1. The speed of the combined mass immediately after the collision with respect to an observer on the ground.
2. The length L of the string such that the tension in the string becomes zero when the string becomes horizontal during the subsequent motion of the combined mass.
Two blocks of mass m1 = 10 Kg and m2 = 5 Kg connected to each other by a massless inextensible string of length 0.3 m are placed along a diameter of turn table. The coefficient of friction between the table and m1 is 0.5 while there is no friction between m2 and the table. The table is rotating with an angular velocity of 10 rad/s about a vertical axis passing through its centre O. The masses are placed along the diameter of the table on either side of the centre O such that the mass m1 is at a distant of 0.124 m from O. The masses are observed to be at rest with respect to an observer on the turn table.
3. Calculate the frictional force on m1.
4. What should be the minimum angular speed of the turn tale so that the masses will slip from this position.
5. How should the masses be placed with the string remaining taut so that there is no frictional force acting on the mass m1.
Source: 1997 JEE paper
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