The length of metallic wire is ${\mathcal{l}}_1$ when tension in it is $T_1$ . It is ${\mathcal{l}}_2$ when the tension is T₂. The original length of the wire will be

A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1.4. Vessel is moving with speed $\upsilon$ and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the gas increases by:

(R = universal gas constant)

In an experiment to determine the Young’s modulus of wire of a length exactly 1m, the extension in the length of the wire is measured as 0.4mm with an uncertainty of $\pm$ 0.02mm when a load of 1kg is applied. The diameter of the wire is measured as 0.4mm with an uncertainty of $\pm$ 0.02mm. The error in the measurement of Young’s modulus $\left(\Delta Y\right)$ is found to be x × 10¹⁰Nm^-2. The value of x is _________.

(take g = 10 ms^-2)

A closely wounded circular coil of radius 5cm produces a magnetic field of 37.68 × 104 T at its centre. The current through the coil is_ A. [Given, number of turns in the coil is 100 and = 3.14]

The pressure P1 and density d1 of diatomic gas $\left(\gamma =\frac{7}{5}\right)$ changes suddenly to P2(>P1) and d2 respectively during an adiabatic process. The temperature of the gas increases and becomes ________times of its initial temperature. (given $\frac{d_2}{d_1}=32)$

Given below are two statements : One is labeled as Assertion (A) and the other is labeled as Reason (R).

Assertion (A) : Clothes containing oil grease statins cannot be cleaned by water wash.

Reason (R) : Because the angle of contact between the oil/grease and water is obtuse.

In the light of the above statements, choose the correct answer from the option given below.