Which of the following statements are
Question: Which of the following statements are true for a stationary wave? (a) every particle has a fixed amplitude which is different from the amplitude of its nearest particle (b) all the particles cross their mean position at the same time (c) all the particles are oscillating with the same amplitude (d) there is no net transfer of energy across any plane (e) there are some particles which are always at rest Solution: The correct answers are (a) every particle has a fixed amplitude which is ...
Read More →A train, standing in a station yard,
Question: A train, standing in a station yard, blows a whistle of frequency 400 Hz in still air. The wind starts blowing in the direction from the yard to the station with a speed of 10 m/s. Given that the speed of sound in still air is 340 m/s (a) the frequency of sound as heard by an observer standing on the platform is 400 Hz (b) the speed of sound for the observer standing on the platform is 350 m/s (c) the frequency of sound as heard by the observer standing on the platform will increase (d...
Read More →At what point of the curve
Question: At what point of the curve $y=x^{2}$ does the tangent make an angle of $45^{\circ}$ with the $x$-axis? Solution: Given: The curve is $y=x^{2}$ Differentiating the above w.r.t $\mathrm{x}$ $\Rightarrow y=x^{2}$ $\Rightarrow \frac{d y}{d x}=2 x^{2}-1$ $\Rightarrow \frac{d y}{d x}=2 x \ldots(1)$ $\therefore \frac{\mathrm{dy}}{\mathrm{dx}}=$ The Slope of the tangent $=\tan \theta$ Since, the tangent make an angle of $45^{\circ}$ with $x$ - axis i.e, $\Rightarrow \frac{d y}{d x}=\tan \left(...
Read More →The transverse displacement of a string
Question: The transverse displacement of a string is given by y(x,t) = 0.06 sin (2x/3) cos (120t). All the points on the string between two consecutive nodes vibrate with (a) same frequency (b) same phase (c) same energy (d) different amplitude Solution: The correct answers are (a) same frequency (b) same phase (d) different amplitude...
Read More →During propagation of a plane
Question: During propagation of a plane progressive mechanical wave (a) all the particles are vibrating in the same phase (b) amplitude of all the particles is equal (c) particles of the medium executes SHM (d) wave velocity depends upon the nature of the medium Solution: The correct answers are (b) amplitude of all the particles is equal (c) particles of the medium executes SHM (d) wave velocity depends upon the nature of the medium...
Read More →Speed of sound waves in a fluid
Question: Speed of sound waves in a fluid depends upon (a) directly on the density of the medium (b) square of bulk modulus of the medium (c) inversely on the square root of density (d) directly on the square root of bulk modulus of the medium Solution: The correct answers are (c) inversely on the square root of density (d) directly on the square root of bulk modulus of the medium...
Read More →The displacement of a string is given by
Question: The displacement of a string is given by y(x,t) = 0.06 sin (2x/3) cos (120t) 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 10-2kg. (a) it represents a progressive wave of frequency 60 Hz (b) it represents a stationary wave of frequency 60 Hz (c) it is the result of the superposition of two waves of wavelength 3 m, frequency 60 Hz each travelling with a speed of 180 m/s in the opposite direction (d) amplitude of this wave is constant Solution: ...
Read More →At what point on the circle
Question: At what point on the circle $x^{2}+y^{2}-2 x-4 y+1=0$, the tangent is parallel to $x$ - axis. Solution: Given: The curve is $x^{2}+y^{2}-2 x-4 y+1=0$ Differentiating the above w.r.t $x$ $\Rightarrow x^{2}+y^{2}-2 x-4 y+1=0$ $\Rightarrow 2 x^{2}-1+2 y^{2}-1 \times \frac{d y}{d x}-2-4 x \frac{d y}{d x}+0=0$ $\Rightarrow 2 x+2 y \frac{d y}{d x}-2-4 \frac{d y}{d x}=0$ $\Rightarrow \frac{\mathrm{d} y}{\mathrm{dx}}(2 y-4)=-2 x+2$ $\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{-2(\mathrm{...
Read More →A transverse harmonic wave on a string
Question: A transverse harmonic wave on a string is described by y (x,t) = 3.0 sin (36t + 0.018x + /4) where x and y are in cm and t is in s. The positive direction of x is from left to right (a) the wave is travelling from right to left (b) the speed of the wave is 20 m/s (c) frequency of the wave is 5.7 Hz (d) the least distance between two successive crests in the wave is 2.5 cm Solution: The correct answers are (a) the wave is travelling from right to left (b) the speed of the wave is 20 m/s...
Read More →A string of mass 2.5 kg is under a tension of 200 N.
Question: A string of mass 2.5 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, the disturbance will reach the other end in (a) one second (b) 0.5 second (c) 2 seconds (d) data given is insufficient Solution: The correct answer is (b) 0.5 second...
Read More →Equation of a plane progressive wave
Question: Equation of a plane progressive wave is given by y = 0.6 sin 2(t-x/2). On reflection from a denser medium, its amplitude becomes 2/3 of the amplitude of the incident wave (a) y = 0.6 sin 2(t+x/2) (b) y = -0.4 sin 2(t+x/2) (c) y = 0.4 sin 2(t+x/2) (d) y = -0.4 sin 2(t-x/2) Solution: The correct answer is (b) y = -0.4 sin 2(t+x/2)...
Read More →A sound wave is passing through
Question: A sound wave is passing through the air column in the form of compression and rarefaction. In consecutive compressions and rarefactions, (a) density remains constant (b) Boyles law is obeyed (c) bulk modulus of air oscillates (d) there is no transfer of heat Solution: The correct answer is (d) there is no transfer of heat...
Read More →Which of the following statements
Question: Which of the following statements are true for wave motion? (a) mechanical transverse waves can propagate through all mediums (b) longitudinal waves can propagate through solids only (c) mechanical transverse waves can propagate through solids only (d) longitudinal waves can propagate through a vacuum Solution: The correct answer is (c) mechanical transverse waves can propagate through solids only...
Read More →Find a point on the curve
Question: Find a point on the curve $y=x^{2}$ where the Slope of the tangent is equal to the $x$-coordinate of the point. Solution: Given: The curve is $y=x^{2}$ $y=x^{2}$ Differentiating the above w.r.t $x$ $\Rightarrow \frac{d y}{d x}=2 x^{2-1}$ $\Rightarrow \frac{d y}{d x}=2 x \ldots(1)$ Also given the Slope of the tangent is equal to the $x$-coordinate, $\frac{\mathrm{dy}}{\mathrm{dx}}=x \ldots(2)$ From (1) \ (2), we get, i.e, $2 x=x$ $\Rightarrow x=0$ Substituting this in $y=x^{2}$, we get,...
Read More →With the propagation of longitudinal
Question: With the propagation of longitudinal waves through a medium, the quantity transmitted is (a) matter (b) energy (c) energy and matter (d) energy, matter, and momentum Solution: The correct answer is (b) energy...
Read More →Change in temperature of
Question: Change in temperature of the medium changes (a) frequency of sound waves (b) amplitude of sound waves (c) wavelength of sound waves (d) loudness of sound waves Solution: The correct answer is (c) wavelength of sound waves...
Read More →Speed of sound wave in air
Question: Speed of sound wave in air (a) is independent of temperature (b) increases with pressure (c) increases with an increase in humidity (d) decreases with an increase in humidity Solution: The correct answer is (c) increases with an increase in humidity...
Read More →Sound waves of wavelength λ travelling
Question: Sound waves of wavelength travelling in a medium with a speed of v m/s enter into another medium where its speed is 2v m/s. The wavelength of sound waves in the second medium is (a) (b) /2 (c) 2 (d) 4 Solution: The correct answer is (c) 2...
Read More →Find a point on the curve
Question: Find a point on the curve $x y+4=0$ at which the tangents are inclined at an angle of $45^{\circ}$ with the $x$-axis. Solution: Given: The curve is $x y+4=0$ If a tangent line to the curve $y=f(x)$ makes an angle $\boldsymbol{\theta}$ with $x$-axis in the positive direction, then $\frac{\mathrm{d} y}{\mathrm{dx}}=$ The Slope of the tangent $=\tan \theta$ $x y+4=0$ Differentiating the above w.r.t $x$ $\Rightarrow x \times \frac{d}{d x}(y)+y \times \frac{d}{d x}(x)+\frac{d}{d x}(4)=0$ $\...
Read More →Water waves produced by a motorboat
Question: Water waves produced by a motorboat sailing in water are (a) neither longitudinal nor transverse (b) both longitudinal and transverse (c) only longitudinal (d) only transverse Solution: The correct answer is (b) both longitudinal and transverse...
Read More →Find the principal solutions of each of the following equations:
Question: Find the principal solutions of each of the following equations: (i) $\sin x=\frac{\sqrt{3}}{2}$ (ii) $\cos \mathrm{x}=\frac{1}{2}$ (iii) $\tan \mathrm{x}=\sqrt{3}$ (iv) $\cot \mathrm{x}=\sqrt{3}$ (v) $\operatorname{cosec} x=2$ (vi) $\sec x=\frac{2}{\sqrt{3}}$ Solution: To Find: Principal solution. [NOTE: The solutions of a trigonometry equation for which 0 x 2 ???? is called principal solution] (i) Given: $\sin x=\frac{\sqrt{3}}{2}$ Formula used: $\sin \theta=\sin \alpha \Rightarrow \...
Read More →Find a point on the curve
Question: Find a point on the curve $y^{2}=2 x^{3}$ at which the Slope of the tangent is 3 Solution: Given: The curve $y^{2}=2 x^{3}$ and The Slope of tangent is 3 $y^{2}=2 x^{3}$ Differentiating the above w.r.t $x$ $\Rightarrow 2 y^{2}-1 \times \frac{d y}{d x}=2 \times 3 x^{3-1}$ $\Rightarrow y \frac{d y}{d x}=3 x^{2}$ $\Rightarrow \frac{d y}{d x}=\frac{3 x^{2}}{y}$ Since, The Slope of tangent is 3 $\frac{3 x^{2}}{y}=3$ $\Rightarrow \frac{x^{2}}{y}=1$ $\Rightarrow x^{2}=y$ Substituting $x^{2}=y...
Read More →Find a point on the curve
Question: Find a point on the curve $y^{2}=2 x^{3}$ at which the Slope of the tangent is 3 Solution: Given: The curve $y^{2}=2 x^{3}$ and The Slope of tangent is 3 $y^{2}=2 x^{3}$ Differentiating the above w.r.t $x$ $\Rightarrow 2 y^{2}-1 \times \frac{d y}{d x}=2 \times 3 x^{3-1}$ $\Rightarrow y \frac{d y}{d x}=3 x^{2}$ $\Rightarrow \frac{d y}{d x}=\frac{3 x^{2}}{y}$ Since, The Slope of tangent is 3 $\frac{3 x^{2}}{y}=3$ $\Rightarrow \frac{x^{2}}{y}=1$ $\Rightarrow x^{2}=y$ Substituting $x^{2}=y...
Read More →Consider a pair of identical pendulums,
Question: Consider a pair of identical pendulums, which oscillate with equal amplitude independently such that when one pendulum is at its extreme position making an angle of 2oto the right with the vertical, the other pendulum makes an angle of 1oto the left of the vertical. What is the phase difference between the pendulums? Solution: 1= 0sin (wt + 1) 2= 0sin (wt + 2) for first, = 2o for second, = -1o 1 2= 120o...
Read More →A mass of 2 kg is attached to the spring
Question: A mass of 2 kg is attached to the spring of spring constant 50 N/m. 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. Solution: x = 5 sin 5t...
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