Answer:
0.495 m/s
Explanation:
[tex]T[/tex] = tension force in the string connecting the two objects
[tex]M[/tex] = Mass of the object on inclined plane = 250 g = 0.250 kg
[tex]m[/tex] = Mass of the hanging object = 150 g = 0.150 kg
[tex]a[/tex] = acceleration of each object
From the force diagram, force equation for the motion of the object on the inclined plane is given as
[tex]T - Mg Sin30 = Ma\\T = Mg Sin30 + Ma[/tex]
From the force diagram, force equation for the motion of the hanging object on the inclined plane is given as
[tex]mg - T = ma\\T = mg - ma[/tex]
Using the above two equations
[tex]Mg Sin30 + Ma = mg - ma[/tex]
[tex](0.250)(9.8) Sin30 + (0.250) a = (0.150) (9.8) - (0.150)a[/tex]
[tex]a = 0.6125 ms^{-2}[/tex]
[tex]h[/tex] = height dropped by the hanging object = 10 cm = 0.10 m
[tex]v[/tex] = Speed gained by the object
Speed gained by the object can be given as
[tex]v = sqrt(2ah)\\v = sqrt(2(0.6125)(0.20))\\v = 0.495 ms^{-1}[/tex]
