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Answer the following questions : (a) Time period of a particle in SHM depends on the force constant k and mass m of the particle: `T=2πsqrt(m/k)`. A simple pendulum executes SHM approximately. Why then is the time period of a pendulum independent of the mass of the pendulum? (b) The motion of a simple pendulum is approximately simple harmonic for small angle oscillations. For larger angles of oscillation, a more involved analysis shows that T is greater than `2πsqrt(l/g)`.Think of a qualitative argument to appreciate this result. (c) A man with a wristwatch on his hand falls from the top

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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A simple pendulum of length l and having a bob of mass M is suspended in a car. The car is moving on a circular track of radius R with a uniform speed v. If the pendulum makes small oscillations in a radial direction about its equilibrium position, what will be its time period

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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A cylindrical piece of cork of density of base area A and height h floats in a liquid of density `ρ_l`. The cork is depressed slightly and then released. Show that the cork oscillates up and down simple harmonically with a period `T=2πsqrt((hρ)/(ρ_lg))` where ρ is the density of cork. (Ignore damping due to viscosity of the

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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One end of a U-tube containing mercury is connected to a suction pump and the other end to atmosphere. A small pressure difference is maintained between the two columns. Show that, when the suction pump is removed, the column of mercury in the U-tube executes simple harmonic

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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An air chamber of volume V has a neck area of cross section a into which a ball of mass m just fits and can move up and down without any friction (Fig.). Show that when the ball is pressed down a little and released , it executes SHM. Obtain an expression for the time period of oscillations assuming pressure-volume variations of air to be isothermal [see Fig. 14.27].

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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You are riding in an automobile of mass 3000 kg. Assuming that you are examining the oscillation characteristics of its suspension system. The suspension sags 15 cm when the entire automobile is placed on it. Also, the amplitude of oscillation decreases by 50% during one complete oscillation. Estimate the values of (a) the spring constant k and (b) the damping constant b for the spring and shock absorber system of one wheel, assuming that each wheel supports 750

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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Show that for a particle in linear SHM the average kinetic energy over a period of oscillation equals the average potential energy over the same

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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A circular disc of mass 10 kg is suspended by a wire attached to its centre. The wire is twisted by rotating the disc and released. The period of torsional oscillations is found to be 1.5 s. The radius of the disc is 15 cm. Determine the torsional spring constant of the wire. (Torsional spring constant α is defined by the relation J = –α θ , where J is the restoring couple and θ the angle of

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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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 (a) 5 cm (b) 3 cm (c) 0

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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A mass attached to a spring is free to oscillate, with angular velocity ω, in a horizontal plane without friction or damping. It is pulled to a distance `x_0` and pushed towards the centre with a velocity `v_0` at time t = 0. Determine the amplitude of the resulting oscillations in terms of the parameters ω, `x_0` and `v_0`. [Hint : Start with the equation x = a cos (ωt+θ) and note that the initial velocity is

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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Given below are some examples of wave motion. State in each case if the wave motion is transverse, longitudinal or a combination of both: (a) Motion of a kink in a longitudinal spring produced by displacing one end of the spring sideways. (b) Waves produced in a cylinder containing a liquid by moving its piston back and forth. (c) Waves produced by a motorboat sailing in water. (d) Ultrasonic waves in air produced by a vibrating quartz

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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A steel wire 0.72 m long has a mass of `5.0 ×10^(–3)` kg. If the wire is under a tension of 60 N, what is the speed of transverse waves on the wire

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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Estimate the speed of sound in air at standard temperature and pressure. The mass of 1 mole of air is `29.0 ×10^(–3)`

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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A pipe, 30.0 cm long, is open at both ends. Which harmonic mode of the pipe resonates a 1.1 kHz source? Will resonance with the same source be observed if one end of the pipe is closed ? Take the speed of sound in air as 330 m

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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Two sitar strings A and B playing the note ‘Dha’ are slightly out of tune and produce beats of frequency 5 Hz. The tension of the string B is slightly increased and the beat frequency is found to decrease to 3 Hz. What is the original frequency of B if the frequency of A is 427 Hz

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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A rocket is moving at a speed of 200 m `s^(–1)` towards a stationary target. While moving, it emits a wave of frequency 1000 Hz. Some of the sound reaching the target gets reflected back to the rocket as an echo. Calculate (1) the frequency of the sound as detected by the target and (2) the frequency of the echo as detected by the

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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A string of mass 2.50 kg is under a tension of 200 N. The length of the stretched string is 20.0 m. If the transverse jerk is struck at one end of the string, how long does the disturbance take to reach the other

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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A stone dropped from the top of a tower of height 300 m splashes into the water of a pond near the base of the tower. When is the splash heard at the top given that the speed of sound in air is 340 m `s^(–1)` ? (g = 9.8 m

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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A steel wire has a length of 12.0 m and a mass of 2.10 kg. What should be the tension in the wire so that speed of a transverse wave on the wire equals the speed of sound in dry air at 20 °C = 343 m

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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Use the formula `v=sqrt((γP)/ρ)` to explain why the speed of sound in air (a) is independent of pressure, (b) increases with temperature, (c) increases with

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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