Which of the following statements is true?

The length of an elastic string is $a$ metres when the longitudinal tension is $4 \ N$ and $b$ metres when the longitudinal tension is $5 \ N$. The length of the string in metres when the longitudinal tension is $9 \ N$ is

The pressure and density of a given mass of a diatomic gas $\left(\gamma = \frac{7}{5}\right)$ change adiabatically from $(P, d)$ to $(P^{\prime}, d^{\prime})$. If $\frac{d^{\prime}}{d} = 32$,then $\frac{P^{\prime}}{P}$ is $(\gamma = \text{ratio of specific heats})$

The angle between the curves $y = \sin x$ and $y = \cos x$ is

$A$ disc has mass $m$ and radius $R$. How much tangential force should be applied to the rim of the disc so as to rotate it with angular velocity $\omega$ in time $t$?

$A$ galvanometer,having a resistance of $50 \Omega$,gives a full-scale deflection for a current of $0.05 \text{ A}$. The length in metres of a resistance wire of cross-sectional area $2.97 \times 10^{-2} \text{ cm}^2$ that can be used to convert the galvanometer into an ammeter which can read a maximum of $5 \text{ A}$ current is: (Specific resistance of the wire $= 5 \times 10^{-7} \Omega\text{-m}$)