The hydraulic press shown in the figure is used to raise the mass M through a height of `0.5 cm` by performing `500J` of work at the small piston. The diameter of the large piston is `10cm`, while that of the smaller one is `2 cm`. The mass M is

Options

A. `100kg`
B. `10^(6)kg`
C. `10^(3)kg`
D. None of these

Answer

D

Explanation

Diameter of left hand side is `(1)/(5)` times. So area will be `(1)/(25)` times.
`Deltap_(LHS) =Delta p_(RHS)implies (F)/((A//25))=((Mg))/(A)`
`:. F=(Mg)/(A)`
Equating the volumes
Displacement of `LHS=5` times
Displacement of RHS
`:. S=(5)(0.5)=2.5cm`
`:. (500)=((Mg)/(25))(2.5xx10^(-2))`
`:. M=5xx10^(4)kg` (with `g=10m//s^(2)`.