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

A body is performing S.H.M. Then its ______.

1. average total energy per cycle is equal to its maximum kinetic energy.
2. average kinetic energy per cycle is equal to half of its maximum kinetic energy.
3. mean velocity over a complete cycle is equal to `2/π` times of its π maximum velocity. 
4. root mean square velocity is times of its maximum velocity `1/sqrt(2)`.

Displacement versus time curve for a particle executing S.H.M. is shown in figure. Identify the points marked at which (i) velocity of the oscillator is zero, (ii) speed of the oscillator is maximum.

Draw a graph to show the variation of P.E., K.E. and total energy of a simple harmonic oscillator with displacement.

Find the displacement of a simple harmonic oscillator at which its P.E. is half of the maximum energy of the oscillator.

A mass of 2 kg is attached to the spring of spring constant 50 Nm^–1. The block is pulled to a distance of 5 cm from its equilibrium position at x = 0 on a horizontal frictionless surface from rest at t = 0. Write the expression for its displacement at anytime t.

A body of mass m is attached to one end of a massless spring which is suspended vertically from a fixed point. The mass is held in hand so that the spring is neither stretched nor compressed. Suddenly the support of the hand is removed. The lowest position attained by the mass during oscillation is 4 cm below the point, where it was held in hand.

What is the amplitude of oscillation?

Water waves produced by a motor boat sailing in water are ______.

The displacement of a string is given by y (x, t) = 0.06 sin (2πx/3) cos (120 πt) where x and y are in m and t in s. The length of the string is 1.5 m and its mass is 3.0 × 10⁻² kg.

1. It represents a progressive wave of frequency 60 Hz.
2. It represents a stationary wave of frequency 60 Hz.
3. It is the result of superposition of two waves of wavelength 3 m, frequency 60 Hz each travelling with a speed of 180 m/s in opposite direction.
4. Amplitude of this wave is constant.

The transverse displacement of a string (clamped at its both ends) is given by y(x, t) = 0.06 sin (2πx/3) cos (120 πt). All the points on the string between two consecutive nodes vibrate with ______.

1. same frequency
2. same phase
3. same energy
4. different amplitude.

Which of the following statements are true for a stationary wave?

1. Every particle has a fixed amplitude which is different from the amplitude of its nearest particle.
2. All the particles cross their mean position at the same time.
3. All the particles are oscillating with same amplitude.
4. There is no net transfer of energy across any plane.
5. There are some particles which are always at rest.

A sonometer wire is vibrating in resonance with a tuning fork. Keeping the tension applied same, the length of the wire is doubled. Under what conditions would the tuning fork still be is resonance with the wire?

An organ pipe of length L open at both ends is found to vibrate in its first harmonic when sounded with a tuning fork of 480 Hz. What should be the length of a pipe closed at one end, so that it also vibrates in its first harmonic with the same tuning fork?

A pipe 20 cm long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a source of 1237.5 Hz? (sound velocity in air = 330 ms^–1)

The wave pattern on a stretched string is shown in figure. Interpret what kind of wave this is and find its wavelength.

The pattern of standing waves formed on a stretched string at two instants of time are shown in figure. The velocity of two waves superimposing to form stationary waves is 360 ms^–1 and their frequencies are 256 Hz.

1. Calculate the time at which the second curve is plotted.
2. Mark nodes and antinodes on the curve.
3. Calculate the distance between A′ and C′.

A tuning fork vibrating with a frequency of 512 Hz is kept close to the open end of a tube filled with water (Figure). The water level in the tube is gradually lowered. When the water level is 17 cm below the open end, maximum intensity of sound is heard. If the room temperature is 20°C, calculate

1. speed of sound in air at room temperature
2. speed of sound in air at 0°C
3. if the water in the tube is replaced with mercury, will there be any difference in your observations?

Show that when a string fixed at its two ends vibrates in 1 loop, 2 loops, 3 loops and 4 loops, the frequencies are in the ratio 1:2:3:4.

A great physicist of this century (P.A.M. Dirac) loved playing with numerical values of Fundamental constants of nature. This led him to an interesting observation. Dirac found that from the basic constants of atomic physics (c, e, mass of electron, mass of proton) and the gravitational constant G, he could arrive at a number with the dimension of time. Further, it was a very large number, its magnitude being close to the present estimate on the age of the universe (~15 billion years). From the table of fundamental constants in this book, try to see if you too can construct this number (or any other interesting number you can think of). If its coincidence with the age of the universe were significant, what would this imply for the constancy of fundamental constants?

A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time t is proportional to ______.

A person trying to lose weight (dieter) lifts a 10 kg mass, one thousand times, to a height of 0.5 m each time. Assume that the potential energy lost each time she lowers the mass is dissipated.

1. How much work does she do against the gravitational force?
2. Fat supplies 3.8 x 10⁷J of energy per kilogram which is converted to mechanical energy with a 20% efficiency rate. How much fat will the dieter use up?