Correct Answer - A
When the gas is heated it expands `&` pushes the piston by x. If k is force constanat of spring and `A` is area of crossection of the piston. It `P_(0)` is atmospheric pressure then at equilibrium of piston the pressure of the gas on the piston
`P=P_(0)+(kx)/(A)`
The increas in the volume of the gas by samll movement of x of piston is
`dv=Adx`
`W=int_(0)^(X)Pdv=P_(0)Ax+(1)/(2)kx^(2)`
Putting `A=4xx10^(-3)m^(2),x=0.1m, W=50 J`.
`P_(0)=1.013xx10^(5) Nm^(-2)` in above equation
`:. k=1896 Nm^(-1)`