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An inextensible string is passing over a light pulley. One end of the string is connected to a block of mass 4m which is resting on a horizontal surface. To another end a plate of mass m is attached and is hanging in the air. A particle of mass m strikes from above with vertical velocity v` and sticks to the plate. Calculate maximum height attained by block of mass 4m.

An inextensible string is passing over a light pulley. One end of the string is connected to a block of mass 4m which is resting on a horizontal surface. To another end a plate of mass m is attached and is hanging in the air. A particle of mass m strikes from above with vertical velocity v` and sticks to the plate. Calculate maximum height attained by block of mass 4m.

Grade:11

1 Answers

Vikas TU
14149 Points
7 years ago
Since Tension forces are acting on the blocks therfore momentum cannot be conserved for individual blocks.
Therefore, For the whole system,
Pi = Pf
mv + 0 = (2m + 4m)v0
v0 = v/6 m/s.
 
From energy conservation,
0.5mv^2 = 6mgx + 0.5mv0^2
v^2/2 = 6gx + 0.5v0^2
put v0 value in the above eqn.
we get,
x = 35v^2/72*6g m. is the displacement.
 

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