﻿ Two small drops of mercury, each of radius R, coalesce to form a

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# 11.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 is1 : 21/3 21/3 : 1 2 : 1 1 : 2

B.

21/3 : 1

Radius of one drop of mercury is R

∴  The volume of one drop =

∴  Total volume of the two drops,

V =  2 ×

V =

Let the radius of the large drop formed be R'

The total volume of the large is also V

R'3 = 2R3

⇒   R' = 21/3 R

Now the surface area of the resultant drop is

S1 = 2 × 4$\mathrm{\pi }$R2

S1 = 8$\mathrm{\pi }$R

and the surface area of the resultant drop is

S2 = 4$\mathrm{\pi }$R'

S2 = 4$\mathrm{\pi }$ 22/3 R2

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

U1 = S1 T

U1 = 8$\mathrm{\pi }$R2T

and the surface energy after coalescing,

U2 = S2

U2 = 22/3 × 4$\mathrm{\pi }$R2T

∴

= $\frac{2}{{2}^{2}{3}}}$

$\frac{{\mathrm{U}}_{1}}{{\mathrm{U}}_{2}}$ = 21/3

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  T1  and  T2 ( T2 >  T1 ). Which of the following plots is correct?

•

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

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