$A$ metal rod of cross-sectional area $10^{-4} \, m^{2}$ is hanging in a chamber kept at $20^{\circ} C$ with a weight attached to its free end. The coefficient of thermal expansion of the rod is $2.5 \times 10^{-6} \, K^{-1}$ and its Young's modulus is $4 \times 10^{12} \, N/m^{2}$. When the temperature of the chamber is lowered to $T$,a weight of $5000 \, N$ needs to be attached to the rod so that its length remains unchanged. Then,$T$ is ............ $^{\circ} C$.

Two blocks of masses $1 \, kg$ and $2 \, kg$ are connected by a metal wire going over a smooth pulley as shown in the figure. The breaking stress of the metal is $2 \times 10^9 \, N/m^2$. What should be the minimum radius of the wire used if it is not to break? Take $g = 10 \, m/s^2$.

Each of three blocks $P$,$Q$ and $R$ shown in the figure has a mass of $3 \,kg$. Each of the wires $A$ and $B$ has a cross-sectional area of $0.005 \,cm^2$ and a Young's modulus of $2 \times 10^{11} \,N \,m^{-2}$. Neglecting friction,the longitudinal strain on wire $B$ is . . . . . . $\times 10^{-4}$. (Take $g=10 \,m/s^2$)

In a series combination of copper and steel wires of same length and same diameter,a force is applied at one of their ends while the other end is kept fixed. The combined length is increased by $2 \ cm$. The wires will have ..........

In order to determine the Young's Modulus of a wire of radius $0.2 \, cm$ (measured using a scale of least count $= 0.001 \, cm$) and length $1 \, m$ (measured using a scale of least count $= 1 \, mm$),a weight of mass $1 \, kg$ (measured using a scale of least count $= 1 \, g$) was hanged to get the elongation of $0.5 \, cm$ (measured using a scale of least count $= 0.001 \, cm$). What will be the fractional error in the value of Young's Modulus determined by this experiment? (in $\%$)

$Assertion :$ Solids are least compressible and gases are most compressible.
$Reason :$ Solids have a definite shape and volume,but gases do not have either a definite shape or a definite volume.