Science (English Medium) Class 11 - CBSE Question Bank Solutions

Consider a given sample of an ideal gas (C_p/C_v = γ) having initial pressure p₀ and volume V₀. (a) The gas is  isothermally taken to a pressure p₀/2 and from there, adiabatically to a pressure p₀/4. Find the final volume. (b) The gas is brought back to its initial state. It is adiabatically taken to a pressure p₀/2 and from there, isothermally to a pressure p₀/4. Find the final volume.

Two samples A and B, of the same gas have equal volumes and pressures. The gas in sample A is expanded isothermally to double its volume and the gas in B is expanded adiabatically to double its volume. If the work done by the gas is the same for the two cases, show that γ satisfies the equation 1 − 2^1−γ = (γ − 1) ln2.

1 litre of an ideal gas (γ = 1.5) at 300 K is suddenly compressed to half its original volume. (a) Find the ratio of the final pressure to the initial pressure. (b) If the original pressure is 100 kPa, find the work done by the gas in the process. (c) What is the change in internal energy? (d) What is the final temperature? (e) The gas is now cooled to 300 K keeping its pressure constant. Calculate the work done during the process. (f) The gas is now expanded isothermally to achieve its original volume of 1 litre. Calculate the work done by the gas. (g) Calculate the total work done in the cycle.

Figure shows a cylindrical tube with adiabatic walls and fitted with an adiabatic separator. The separator can be slid into the tube by an external mechanism. An ideal gas (γ = 1.5) is injected in the two sides at equal pressures and temperatures. The separator remains in equilibrium at the middle. It is now slid to a position where it divides the tube in the ratio 1 : 3. Find the ratio of the temperatures in the two parts of the vessel.

Two vessels A and B of equal volume V₀ are connected by a narrow tube that can be closed by a valve. The vessels are fitted with pistons that can be moved to change the volumes. Initially, the valve is open and the vessels contain an ideal gas (C_p/C_v = γ) at atmospheric pressure p₀ and atmospheric temperature T₀. The walls of vessel A are diathermic and those of B are adiabatic. The valve is now closed and the pistons are slowly pulled out to increase the volumes of the vessels to double the original value. (a) Find the temperatures and pressures in the two vessels. (b) The valve is now opened for sufficient time so that the gases acquire a common temperature and pressure. Find the new values of the temperature and pressure.

The figure shows an adiabatic cylindrical tube of volume V₀ divided in two parts by a frictionless adiabatic separator. Initially, the separator is kept in the middle, an ideal gas at pressure p₁ and temperature T₁ is injected into the left part and another ideal gas at pressure p₂ and temperature T₂ is injected into the right part. C_p/C_v = γ is the same for both the gases. The separator is slid slowly and is released at a position where it can stay in equilibrium. Find (a) the volumes of the two parts (b) the heat given to the gas in the left part and (c) the final common pressure of the gases.

An ideal gas of density 1.7 × 10⁻³ g cm⁻³ at a pressure of 1.5 × 10⁵ Pa is filled in a Kundt's tube. When the gas is resonated at a frequency of 3.0 kHz, nodes are formed at a separation of 6.0 cm. Calculate the molar heat capacities C_p and C_v of the gas.

Given a + b + c + d = 0, state whether the following statement is correct or incorrect:

a, b, c, and d must each be a null vector.

A body describes simple harmonic motion with an amplitude of 5 cm and a period of 0.2 s. Find the acceleration and velocity of the body when the displacement is 5 cm.

A body describes simple harmonic motion with an amplitude of 5 cm and a period of 0.2 s. Find the acceleration and velocity of the body when the displacement is 3 cm.

Measure of two quantities along with the precision of respective measuring instrument is A = 2.5 ms^–1 ± 0.5 ms^–1 B = 0.10 s ± 0.01 s. The value of A B will be ______.

You measure two quantities as A = 1.0 m ± 0.2 m, B = 2.0 m ± 0.2 m. We should report correct value for `sqrt(AB)` as ______.

The mean length of an object is 5 cm. Which of the following measurements is most accurate?

The vernier scale of a travelling microscope has 50 divisions which coincide with 49 main scale divisions. If each main scale division is 0.5 mm, calculate the minimum inaccuracy in the measurement of distance.

Time for 20 oscillations of a pendulum is measured as t₁ = 39.6 s; t₂ = 39.9 s; t₃ = 39.5 s. What is the precision in the measurements? What is the accuracy of the measurement?

A physical quantity X is related to four measurable quantities a, b, c and d as follows: X = a² b³ c^5/2d^–2. The percentage error in the measurement of a, b, c and d are 1%, 2%, 3% and 4%, respectively. What is the percentage error in quantity X? If the value of X calculated on the basis of the above relation is 2.763, to what value should you round off the result.

A ball is dropped from a building of height 45 m. Simultaneously another ball is thrown up with a speed 40 m/s. Calculate the relative speed of the balls as a function of time.

It is a common observation that rain clouds can be at about a kilometre altitude above the ground.

1. If a rain drop falls from such a height freely under gravity, what will be its speed? Also calculate in km/h. ( g = 10 m/s²)
2. A typical rain drop is about 4mm diameter. Momentum is mass x speed in magnitude. Estimate its momentum when it hits ground.
3. Estimate the time required to flatten the drop.
4. Rate of change of momentum is force. Estimate how much force such a drop would exert on you.
5. Estimate the order of magnitude force on umbrella. Typical lateral separation between two rain drops is 5 cm.

(Assume that umbrella is circular and has a diameter of 1 m and cloth is not pierced through !!)

A man is standing on top of a building 100 m high. He throws two balls vertically, one at t = 0 and other after a time interval (less than 2 seconds). The later ball is thrown at a velocity of half the first. The vertical gap between first and second ball is +15 m at t = 2 s. The gap is found to remain constant. Calculate the velocity with which the balls were thrown and the exact time interval between their throw.

A, B and C are three non-collinear, non co-planar vectors. What can you say about direction of A × (B × C)?