If the length of a wire is made double and radius is halved of its respective values. Then, the Young's modulus of the material of wire will :

Option 1 - Remain same

Option 2 - Become 8 times its initial value

Option 3 - Become <math><mrow><msup><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow><mrow><mi>t</mi><mi>h</mi></mrow></msup></mrow></math> of its initial value

Option 4 - Become 4 times its initial value

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A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1.4. Vessel is moving with speed $υ$ 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)

Payal Gupta

$K E = Δ U$

$Δ U = \frac{1}{2} m v^{2}$

$n C_{v} Δ T = \frac{m v^{2}}{2}$

$\Rightarrow \frac{m}{M} \frac{R}{y - 1} Δ T = \frac{m v^{2}}{2}$

$Δ T = \frac{0.4}{2} \frac{M v^{2}}{R}$

$Δ T = \frac{M v^{2}}{5 R}$

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 $(Δ Y)$ is found to be x × 10¹⁰Nm^-2. The value of x is _________.

(take g = 10 ms^-2)

Vishal Baghel

L = 1 m

$Δ L = 0.4 \times 1 0^{- 3} m$

$m = 1 k g$

d = 0.4 × 10^-3 m

$\frac{F}{A} = y \frac{Δ L}{L}$

$y = \frac{F L}{A Δ L} = \frac{(m g) \times 1}{(\frac{π d^{2}}{4}) \times 0.4 \times 1 0^{- 3}}$

$Δ y = 0.1 \times 0.199 \times 1 0^{12} = 1.99 \times 1 0^{10}$

= 1.99

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]

Vishal Baghel

$B_{c e n t r e} = N \frac{μ_{0} i}{2 r}$

$\Rightarrow \frac{100 \times 4 π \times 1 0^{- 7} \times i}{2 \times 5 \times 1 0^{- 2}} = 37.68 \times 1 0^{- 4}$

$∴ i = \frac{37.68}{4 \times 3.14} = 3 A$

The pressure P1 and density d1 of diatomic gas $(γ = \frac{7}{5})$ 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 $\frac{d_{2}}{d_{1}} = 32)$

Vishal Baghel

For adiabatic process – PVY = const

$T_{1} {V_{1}}^{Y - 1} = T_{2} V_{2}^{Y - 1}$

$\frac{T_{2}}{T_{1}} = {(\frac{v_{1}}{v_{2}})}^{Y - 1} = {(\frac{d_{2}}{d_{1}})}^{Y - 1} = {(32)}^{(\frac{7}{5} - 1)} = {(32)}^{2 / 5}$

$= {(2)}^{2} = 4$

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.

Vishal Baghel

Water molecule doesnâ€™t stick with oil/ grease drops due to obtuse angle of contact between then.

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Physics NCERT Exemplar Solutions Class 12th Chapter Nine 2025

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