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(a) Initially, the pressure inside the cylinder is equal to atmospheric pressure as given in question. So, pressure (thus force) on piston will be same from outside the cylinder and inside the cylinder which is atmospheric pressure. Therefore, no net force will act on piston and tension in wire will be zero.

(b)

Given

Initial temperature T₁=T_o

Increased temperature T₂=2T_o

Initial pressure of gas P₁=P_o=10⁵Pa

Let curved surface area of cylinder be A

Let the piston be L distance apart

Volume =arealength=AL

Since, no new gas is added to cylinder so, number of moles, before and after temperature change will be same and the volume of cylinder is same. So, applying ideal gas equation, before and after the increase of temperature.

PV=nRT

Where V= volume of gas

R=gas constant =8.3JK^-1mol^-1

T=temperature

n=number of moles of gas

P=pressure of gas.

P₂=210⁵=2P₁=2P_o

Net pressure P₂-P₁=2P_o-P_o=P_o

Net force acting outwards is force=pressurearea

F=P_oA ……(i)

Since, temperature is increased, gas inside the cylinder will expand and piston will move outward freely without any acceleration, as the piston is frictionless. So, from diagram F>T

From newton second law of motion, which states that ‘net external force on particle is equal to rate of change of momentum’, we can write

F-T=0

Rate of change of momentum will be zero because piston moves without any acceleration. So,

Therefore,

F=T= P_oA ( from (i))

The tension if the temperature is increased to 2T₀ is P_oA.