A wedge of mass M rests with one face in contact with horizontal , smooth surface . A particle of mass m is placed on the smooth face on it , inclined at an angle `alpha`to the horizontal and released . Find the velocity of the wedge and that of the particle relative to the wedge when the particle has slipped a distance x down the face of the wedge . Also calculate the acceleration of the wedge and that of the particle relative to the wedge and the smooth surface .
[Hint : Apply principal of conservation of momentum along the horizontal and energy conservation principle . See Example 8 )

Answer

`sqrt((2 m^(2)g x "sin"alpha cos^(2) alpha)/((M + m) (M + m sin^(2)alpha))) , sqrt((2(M+ m) g x "sin"alpha)/(M + m sin^(2) alpha)) ((M + m) g "sin"alpha)/(M + m sin^(2)alpha) , (mg"sin" alpha "cos"alpha)/(M + m sin^(2) alpha)`