Physics GS TIFR- Tata Institute of Fundamental Research Questions 1-5_ Solved

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1. The diagram below represents a periodic wave. Which point on the wave is 90° out of phase with point P?

(i) A

(ii) B

(iii) C

(iv) D

Answer: To determine which point on a periodic wave is 90° out of phase with a given point P, you would need to find the point on the wave that is one-quarter of the wavelength away from point P. This is because one complete wavelength represents a phase difference of 360°, and one-quarter of a wavelength corresponds to a phase difference of 90°.

2. An electric circuit has two parallel plate capacitors (C1 and C2) in series. Both capacitors have the same dielectric and inter-plate distance, but the plates in C1 have a higher surface area compared to those in C2. Once fully charged, which of the two capacitors will have a higher voltage drop?

C1

C2

(i) The capacitor which is closer to the power supply

(ii) The capacitor which is further from the power supply

Answer: Since the two capacitors are in series, they share the same charge Q, but have different voltage drops V1 and V2. To determine which capacitor has the higher voltage drop, we can use the equation for the equivalent capacitance of capacitors in series:

1/Ceq = 1/C1 + 1/C2

Since C1 has a higher surface area, it will have a higher capacitance than C2, so Ceq will be dominated by C2. Therefore, the voltage drop across C2 will be higher than the voltage drop across C1.

To see this more explicitly, we can use the equation for the voltage drop across a capacitor:

V = Q/C

Since Q is the same for both capacitors and C2 has a lower capacitance than C1, the voltage drop V2 across C2 will be higher than the voltage drop V1 across C1:

V2 = Q/C2 > Q/C1 = V1

So, in summary, the capacitor with the higher surface area (C1) will have a lower voltage drop than the capacitor with the lower surface area (C2).

3. A decibel is a measure of

(i) The ratio of sound amplitude to sound frequency

(ii) The ratio of a pure tone to the background noise

(iii) The frequency of sound

(iv) The amplitude of sound

Answer: A decibel (dB) is a unit of measurement used to express the ratio of two values of a physical quantity, usually power or intensity. It is commonly used to describe the intensity of sound, where the sound level in decibels is a measure of the pressure of sound waves relative to a reference level. The decibel scale is logarithmic, so a change of 10 decibels represents a tenfold increase or decrease in intensity or power.

4. A bullet with the same density as water is shot straight down into a very deep water tank. What happens after sufficient time?

(i) The bullet eventually comes to a halt at an intermediate depth.

(ii) The bullet eventually falls to the bottom of the tank

(iii) The bullet initially moves down but eventually floats to the surface.

(iv) The bullet eventually oscillates between two depths.

Answer: Assuming that the bullet does not have any air pockets or other irregularities that would cause it to float or sink at an angle, the bullet will eventually come to rest at the bottom of the water tank.

This is because the bullet has the same density as water, so it will experience an upward force (buoyancy) equal to the weight of the water it displaces as it falls. This buoyant force will initially slow down the bullet's descent, and eventually, the buoyant force will be equal to the weight of the bullet, causing it to stop moving downward and come to rest at the bottom of the tank.

It's worth noting that the depth of the water tank would have an impact on the amount of time it takes for the bullet to come to rest. The deeper the tank, the longer it would take for the bullet to settle at the bottom, as there would be more water to displace and more resistance to the bullet's motion.

5. Reaction P has ΔH<0 and ΔS>0 while reaction Q has ΔH>0 and ΔS>0. Which of the following is true?

(i) Both P and Q are spontaneous at all temperatures because entropy increases.

(ii) P is spontaneous at all temperatures but Q is spontaneous only at high temperatures.

(iii) P is spontaneous only at high temperatures but Q is spontaneous at all temperatures.

(iv) Both P and Q are spontaneous only at high temperatures.

Answer: Based on the given information, we can use the Gibbs free energy equation to determine the spontaneity of the reactions:

ΔG = ΔH - TΔS

where ΔG is the Gibbs free energy change, ΔH is the enthalpy change, ΔS is the entropy change, and T is the temperature in Kelvin.

For reaction P:

ΔG = ΔH - TΔS

Since ΔH is negative and ΔS is positive, the value of TΔS will be positive at all temperatures. Thus, ΔG will be negative at high temperatures and positive at low temperatures. This means that the reaction is spontaneous at high temperatures (where ΔG is negative) and non-spontaneous at low temperatures (where ΔG is positive).

For reaction Q:

ΔG = ΔH - TΔS

Since ΔH is positive and ΔS is positive, the value of TΔS will be positive at all temperatures. Thus, ΔG will be positive at all temperatures, meaning that the reaction is non-spontaneous at all temperatures.

Therefore, the true statement is that reaction P is spontaneous at high temperatures while reaction Q is non-spontaneous at all temperatures.

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