Two cylinders fitted with pistons and placed as shown, connected with string through a small tube of negligible volume, are filled with gas at pressure `P_(0)` and temperature `T_(0)`. The radius of smaller cylinder is half of the other. If the temperature is increased to `2 T_(0)`, find the pressure if the piston of bigger cylinder moves towards left by 1 metre ?

Options

A. `(4)/(5)P_(0)`
B. `(3)/(5)P_(0)`
C. `(2)/(5)P_(0)`
D. `(5)/(4)P_(0)`

Answer

D

Explanation

Initial volume `=1xx[piR^(2)+(piR^(2))/(4)]=(5)/(4)piR^(2)`
Piston moves towards left by one metre on heating Additional volume available due to heating.
`=1xxpiR^(2)-(1xxpiR^(2))/(4)=(3)/(4)piR^(2)`
Total volume after heating `=2piR^(2)`
`P_(0)xx(5)/(4)piR^(2)=nRT_(0)`
After heating, `P_(2)xx2piR^(2)=nRxx2T_(0)`
`(P_(0)//P_(2))xx(5)/(4)xx(1)/(4)=(1)/(2)(P_(0)//P_(2))xx(5)/(4)xx(1)/(2)=(1)/(2)`
`P_(2)=5p_(0)//4`