The hydraulic press shown in the figure is used to raise the mass `M` through a height of 5.0 mm by performing 500 J of work at the small piston. The diameter of the large piston is 10 cm while that of the smaller one is 2 cm. The mass M is

Options

A. `10^(4)kg`
B. `10^(3)kg`
C. `100kg`
D. `10^(5)kg`

Answer

A

Explanation

Since, M moves `5.0` mm and volume of liquid remains constant
`:. pixx(5xx10^(-2))^(2)(5xx10^(-3))=pixx(1xx10^(-2))^(2)x`
`:. x=125xx10^(-3)m`
Suppose force F does `500J` work on small piston `Fx=500`
`F=(500)/(125xx10^(-3))N=4xx10^(3)N`
Using Pascal's law `Mg=(F(5xx10^(-2))^(2))/((1xx10^(-2))^(2))`
`Mg=100xx10^(3)=10^(5)NimpliesM=10^(4)kg`