Physics Test - 1

The Wheatstone Bridge will be balanced when the ratio of resistances in the two arms is equal. Let us consider the arrangement of the Wheatstone bridge as shown in the figure where resistance S′ makes the Wheatstone bridge balanced as shown in the figure.

It is given in the question that P = 2Ω,Q = 2Ω and R = 2Ω

For this Wheatstone bridge to be balanced the ratio of resistances in the two arms must be equal.

Thus the required resistance must be 2Ω instead of S = 3Ω in order to make the Wheatstone bridge balanced.

For this, the shunt resistance x must be connected in parallel with resistance S = 3Ω to make the resultant resistance 2Ω.

We know that for parallel connection,

Thus, the resistance with which S is to be shunted in order that the bridge may be balanced is 6Ω.

Hence, the correct answer is 6Ω.

You can start by explaining the dimensional formula, heat, temperature and entropy. Remember to mention the dimensional formula of heat and temperature. Then use the equation from the second law of thermodynamics, i.e.  and place the dimensional formula of heat and temperature to reach the solution.

Before attempting the mathematical calculations let's first look at some important concepts.

Dimensional formula - every physical quantity has a unit assigned for it, for example force has a unit kgm/s². When we express this unit in terms of the fundamental quantities we get the dimensional formula of that physical quantity.

Here M represents mass, L represents length, T represents time and K represents temperature.

Heat - It can be more simply understood as heat transfer. It is the measurement of the thermal energy that is transferred when a system having a certain specific heat and mass undergoes a temperature change. Its dimensional formula is 

Temperature - It is a physical quantity that determines how hot or cold an object is. It is an intensive property (a property that depends on the quantity of matter in the system). The dimensional formula of temperature is 

Entropy - Entropy in thermodynamics is defined as an extensive property (a property that depends on the quantity of matter in the system) which determines all the possible configuration a system can have. It is also the measure of the energy that is not available for doing work.

According to the second law of thermodynamics, the change in entropy is equal to the change in the amount of heat divided by the temperature.

So, the dimensional formula of entropy is equal to the dimensional formula of heat divided by the dimensional formula of temperature.

The free-body diagram of the system consisting of the lawn roller and the forces acting on it is drawn as follows.

In this diagram, the horizontal component of the force is represented, as, when the lawn roller is pulled along a horizontal surface, the horizontal component of the force acts on it. The term 'S' represents the distance covered by the lawn roller when pulled by the rope.

Now, we will compute the work done by the pulling force for pulling the lawn roller horizontally.

The equation for the same is given as follows.

The horizontal component of the force acts on the lawn roller.

Thus, the above equation of the work done can be represented as follows.

In the question, we are given the height at which water rises in a capillary tube of a certain diameter. Now the capillary tube is replaced by a similar tube of half the diameter of the previous tube. We are asked to find the height at which water will rise.

In order to answer this let us recall the expression for a surface of the liquid in a capillary tube which is given by,

Where, ℎ is the height at which the liquid rises in the capillary, y is the surface tension of the liquid, r is the radius of the capillary tube, p is the density of the liquid, g is the acceleration due to gravity and 0 is the angle of contact with the surface.

From this relation, we see that the height at which the liquid rises in the capillary is inversely proportional to the radius of the capillary tube, that is,

Let the diameter of the first capillary tube be d₁, its radius be r₁ and the height at which the liquid rises in the tube be ℎ1, then,

Now, let the diameter of the second capillary tube bed 2, its radius be r₂ and the height at which the liquid rises in the tube be ℎ2, then,

But in the question, ℎ1 is given as h, therefore, the height at which the water will rise for a similar tube of half the diameter is found to be 4 h.

Hence, the correct answer is 4 h.

We are given that the Earth is contracted to half its present size. Change in size implies a change in radius, so, here the present radius of earth (�1) is reduced by half.

That is, after contraction the radius becomes,

Due to the above mentioned contraction, the angular velocity of Earth's rotation changes.

Also, we know that angular velocity is given by,

There is another quantity that is undergoing change due to contraction of earth - moment of inertia.

Moment of inertia of a solid sphere is given by,

Now, by the law of conservation of angular momentum,

But we know the present time period rotation of our planet Earth as 24 hours.

The time period of rotation of Earth is what we call a day. 

So, for an Earth that is contracted to half its present size with mass constant, the duration of a day will be just 6Hrs.

Hence, the correct answer is 6 Hrs.

Given:

(i) The formula of the capacitance is given by 

(ii) The formula of the capacitance of the air is given by 

It is given that:

Using the formula of dielectric initially:

Substituting the formula of the capacitance of the air initially in the final capacitance.

The capacitance of the parallel plate capacitor is the sum of the capacitance of the air and the capacitance of the dielectrics.

Here it is given in the question that these two particles execute S.H.M. and both the particles have the same amplitude and frequency, so the equation would be given by,

It is given that these two particles cross paths with each other. Also, their displacement is half of their amplitudes,

Now similarly for x₂ we are given that they are moving in different directions after collision, so the closest value of 

Speed in still water is 5 km/h.

Let the velocity of the river be mkm/h.

Width of the river is 1 km and time taken is 15 minutes, that is 1/4 14 hour.

Now the situation is described below,

If the river had been still, the boat would have moved from A to B,1 km but, the boat moves from A to C.

The covered distance by the river water in 15 minutes is 0.75 km.

Now, the velocity of the river is

Molar heat is that amount of capacity in which heat is needed to raise the temperature of 1 mole of a substance by 1 kelvin or 1^∘C at constant volume.

Here R is the universal gas constant.

Now from the question:

Molar heat capacity at constant volume,