Science (English Medium) इयत्ता ११ - CBSE Question Bank Solutions

Figure shows a source of sound moving along X-axis at a speed of 22 m s⁻¹continuously emitting a sound of frequency 2.0 kHz which travels in air at a speed of 330 m s⁻¹. A listener Q stands on the Y-axis at a distance of 330 m from the origin. At t = 0, the sources crosses the origin P. (a) When does the sound emitted from the source at P reach the listener Q? (b) What will be the frequency heard by the listener at this instant? (c) Where will the source be at this instant?

A source of sound emitting a 1200 Hz note travels along a straight line at a speed of 170 m s⁻¹. A detector is placed at a distance 200 m from the line of motion of the source. (a) Find the frequency of sound receive by the detector at the instant when the source gets closest to it. (b) Find the distance between the source and the detector at the instant in detects the frequency 1200 Hz. Velocity of sound in air = 340 m s⁻¹.

A small source of sound S of frequency 500 Hz is attached to the end of a light string and is whirled in a vertical circle of radius 1.6 m. The string just remains tight when the source is at the highest point. (a) An observer is located in the same vertical plane at a large distance and at the same height as the centre of the circle. The speed of sound in air = 330 m s⁻¹ and g = 10 m s⁻². Find the maximum frequency heard by the observer. (b) An observer is situated at a large distance vertically above the centre of the circle. Find the frequency heard by the observer corresponding to the sound emitted by the source when it is at the same height as the centre.

A person stands on a spring balance at the equator. If the speed of earth's rotation is increased by such an amount that the balance reading is half the true weight, what will be the length of the day in this case?

One end of a metal rod is dipped in boiling water and the other is dipped in melting ice.

In summer, a mild wind is often found on the shore of a clam river. This is caused due to

Answer the following question.

Show that its time period is given by, 2π`sqrt((l cos theta)/("g"))` where l is the length of the string, θ is the angle that the string makes with the vertical, and g is the acceleration due to gravity.

Answer the following question.

Define the binding energy of a satellite.

On the basis of dimensions, decide which of the following relations for the displacement of a particle undergoing simple harmonic motion is not correct ______.

1. y = `a sin  (2πt)/T`
2. y = `a sin vt`
3. y = `a/T sin (t/a)`
4. y = `asqrt(2) (sin  (2pit)/T - cos  (2pit)/T)`

If P, Q, R are physical quantities, having different dimensions, which of the following combinations can never be a meaningful quantity?

1. (P – Q)/R
2. PQ – R
3. PQ/R
4. (PR – Q²)/R
5. (R + Q)/P

A function f(θ) is defined as: `f(θ) = 1 - θ + θ^2/(2!) - θ^3/(3!) + θ^4/(4!)` Why is it necessary for q to be a dimensionless quantity?

Why length, mass and time are chosen as base quantities in mechanics?

Give an example of a physical quantity which has a unit but no dimensions.

Give an example of a physical quantity which has neither unit nor dimensions.

The volume of a liquid flowing out per second of a pipe of length l and radius r is written by a student as `v = π/8 (pr^4)/(ηl)` where P is the pressure difference between the two ends of the pipe and η is coefficient of viscosity of the liquid having dimensional formula ML^–1 T^–1. Check whether the equation is dimensionally correct.

In the expression P = E l² m^–5 G^–2, E, m, l and G denote energy, mass, angular momentum and gravitational constant, respectively. Show that P is a dimensionless quantity.

If velocity of light c, Planck’s constant h and gravitational contant G are taken as fundamental quantities then express mass, length and time in terms of dimensions of these quantities.

An artificial satellite is revolving around a planet of mass M and radius R, in a circular orbit of radius r. From Kepler’s Third law about the period of a satellite around a common central body, square of the period of revolution T is proportional to the cube of the radius of the orbit r. Show using dimensional analysis, that `T = k/R sqrt(r^3/g)`. where k is a dimensionless constant and g is acceleration due to gravity.

Einstein’s mass-energy relation emerging out of his famous theory of relativity relates mass (m ) to energy (E ) as E = mc², where c is speed of light in vacuum. At the nuclear level, the magnitudes of energy are very small. The energy at nuclear level is usually measured in MeV, where 1 MeV= 1.6 × 10^–13 J; the masses are measured in unified atomic mass unit (u) where 1u = 1.67 × 10^–27 kg.

1. Show that the energy equivalent of 1 u is 931.5 MeV.
2. A student writes the relation as 1 u = 931.5 MeV. The teacher points out that the relation is dimensionally incorrect. Write the correct relation.

A uniformly moving cricket ball is turned back by hitting it with a bat for a very short time interval. Show the variation of its acceleration with time. (Take acceleration in the backward direction as positive).