Physics

NEET Class 12

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Two small drops of mercury, each of radius R, coalesce to form a single large drop. The ratio of the total surface energies before and after change is

1 : 2

^{1/3}2

^{1/3}: 12 : 1

1 : 2

B.

2^{1/3} : 1

Radius of one drop of mercury is R

∴ The volume of one drop = $\frac{4}{3}\mathrm{\pi}{\mathrm{R}}^{3}$

∴ Total volume of the two drops,

V = 2 × $\frac{4}{3}\mathrm{\pi}{\mathrm{R}}^{3}$

V = $\frac{8}{3}{\mathrm{\pi R}}^{3}$

Let the radius of the large drop formed be R'

The total volume of the large is also V

$\frac{4}{3}\mathrm{\pi}\mathrm{R}{\text{'}}^{2}=\frac{8}{3}\mathrm{\pi}{\mathrm{R}}^{3}$

R'^{3} = 2R^{3}

⇒ R' = 2^{1/3} R

Now the surface area of the resultant drop is

S_{1}_{ }= 2 × 4$\mathrm{\pi}$R^{2}

S_{1}_{ }= 8$\mathrm{\pi}$R^{2 }

and the surface area of the resultant drop is

S_{2} = 4$\mathrm{\pi}$R'^{2 }

S_{2} = 4$\mathrm{\pi}$ 2^{2/3 }R^{2}

Let T be the surface tension of the mercury. Therefore the surface energy of the two drops before coalescing is

U_{1} = S_{1} T

U_{1}_{ }= 8$\mathrm{\pi}$R^{2}T

and the surface energy after coalescing,

U_{2} = S_{2}T

U_{2}_{ }= 2^{2/3} × 4$\mathrm{\pi}$R^{2}T

∴ $\frac{{\mathrm{U}}_{1}}{{\mathrm{U}}_{2}}=\frac{8\mathrm{\pi}{\mathrm{R}}^{2}\mathrm{T}}{{2}^{{\displaystyle \raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}\times 4\mathrm{\pi}{\mathrm{R}}^{2}\mathrm{T}}$

= $\frac{2}{{2}^{{\displaystyle \raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}}$

$\frac{{\mathrm{U}}_{1}}{{\mathrm{U}}_{2}}$ = 2^{1/3}

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12.

A black body, at a temperature of 227^{°}C, radiates heat at a rate of 20 cal m^{-2} s^{-1}. When its temperature is raised to 727^{°}C, the heat radiated by it in cal m^{-2} s^{-1} will be closest to

40

160

320

640

13.

Two springs of force constants k and 2k are connected to a mass as shown in figure . The frequency of oscillation of the mass is

$\frac{1}{2\mathrm{\pi}}\sqrt{\frac{\mathrm{k}}{\mathrm{m}}}$

$\frac{1}{2\mathrm{\pi}}\sqrt{\frac{2\mathrm{k}}{\mathrm{m}}}$

$\frac{1}{2\mathrm{\pi}}\sqrt{\frac{3\mathrm{k}}{\mathrm{m}}}$

$\frac{1}{2\mathrm{\pi}}\sqrt{\frac{\mathrm{m}}{\mathrm{k}}}$

14.

Shown below are the black body radiation curves at temperatures T_{1} and T_{2} ( T_{2} > T_{1} ). Which of the following plots is correct?

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15.

**Assertion: **Temperatures near the sea coast me moderate.

**Reason: **Water has a high thermal conductivity.

If both assertion and reason are true and the reason is the correct explanation of the assertion

If both assertion and reason are true and the reason is not the correct explanation of the assertion

If assertion is true but reason is false

If both assertion and reason are false statements

16.

**Assertion:** When a beetle moves along the sand within a few tens of centimetres of a sand scorpion, the scorpion immediately turns towards the beetle and dashes towards it.

**Reason:** When a beetle disturbs the sand, it sends pulses along the sand's surface. One set of pulses is longitudinal while the other set is transverse.

if both assertion and reason are true and the reason is the correct explanation of the assertion

if both assertion and reason are true and the reason is not the correct explanation of the assertion

if assertion and reason is false

if both assertion and reason are false statements

17.

**Assertion:** When a bottle of cold carbonated drink is opened, a slight fog forms around the opening.

**Reason: ** Adiabatic expansion of the gas causes lowering of temperature and condensation of water vapours.

if both assertion and reason are true and the reason is the correct explanation of the assertion.

if both assertion and reason are true and the reason is not the correct explanation of the assertion.

if assertion is true but reason is false

if both assertion and reason are false statements

18.

**Assertion:** The size of a hydrogen balloon increases as it rises in air.

**Reason:** The material of the balloon can be easily stretched.

if both assertion and reason are true and the reason is the correct explanation of the assertion

if both assertion and reason are true and the reason is not the correct explanation of the assertion

if assertion is true but reason is false

if both assertion and reason are false statements

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19.

**Assertion:** It is hotter over the top of a fire than at the same distance on the sides

**Reason: **Air surrounding the fire conducts more heat upwards.

if both assertion and reason are true and the reason is the correct explanation of the assertion

if both assertion and reason are true and the reason is not the correct explanation of the assertion

if assertion is true but reason is false

if both assertion and reason are false statements

20.

**Assertion: **The amplitude of an oscillating pendulum decreases gradually with time.

**Reason:** The frequency of the pendulum decreases with time.

if both assertion and reason are true and reason is the correct explanation of assertion

if both assertion and reason are true and the reason is not the correct explanation of the assertion

if assertion is true but reason is false

if both assertion and reason are false statements

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