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A boat crosses a river of width 1 km by shortest path in 15 min. If the speed of boat in still water is 5 kmh^-1, then what is the speed of the river?

1) 5 kmh-1 2) 12 kmh-1 3) 3 kmh-1 4) 4 kmh-1 Answer: 3) 3 kmh-1 Solution: Boat crosses a river of width 1 km by shortest path in 15... View Article

If a.b = |a x b|, then θ will be

1) 450 2) 600 3) 750 4) 300 Answer: 450 Solution: a.b = |a x b| |a||b|cos θ = |a||b| sin θ tan θ = 1... View Article

A tuning fork of frequency 440 Hz is attached to a long string of linear mass density 0.01 kg m⁻¹ kept under a tension of 49 N. The fork produces transverse waves of amplitude 0.50 mm on the string.

(a) Find the wave speed and the wavelength of the waves. (b) Find the maximum speed and acceleration of a particle of the string. (c) At what... View Article

A 200 Hz wave with amplitude 1 mm travels on a long string of linear mass density 6 g m⁻¹ kept under a tension of 60 N.

(a) Find the average power transmitted across a given point on the string. (b) Find the total energy associated with the wave in a 20 m long... View Article

A transverse wave of amplitude 0.50 mm and frequency 100 Hz is produced on a wire stretched to a tension of 100 N. If the wave speed is 100 m s⁻¹, what average power is the source transmitting to the wire?

Average power of the source = P = 2π2mva2f2...(1)v = √(T/m) = 100 m/s and m = 0.01 kg/mr = 0.5 x 10-3 and f = 100(Given)On substituting the... View Article

Two long strings A and B, each having linear mass density 12 × 10⁻² kg m⁻¹, are stretched by different tensions 48 N and 75 N respectively and are kept parallel to each other with their left ends at x = 0. Wave pulses are produced on the strings at the left ends at t = 0 on string A and at t = 20 ms on string B. When and where will the pulse on B overtake that on A?

Suppose v and v’ are wave speeds in string A and B respectively. T = 4.8 and m = 1.2 x 10-2 and T' = 7.5 Now, v = √(T/m) = 20 m/s and v' =... View Article

A heavy but uniform rope of length L is suspended from a ceiling.

(a) Write the velocity of a transverse wave travelling on the string as a function of the distance from the lower end. (b) If the rope is given... View Article

A circular loop of string rotates about its axis on a frictionless horizontal plane at a uniform rate so that the tangential speed of any particle of the string is υ. If a small transverse disturbance is produced at a point of the loop, with what speed (relative to the string) will this disturbance travel on the string?

R = Radius of the loop, m = mass per unit length of the stringω = angular velocity, V = linear velocity of the stringThe force for a small potion... View Article

A heavy ball is suspended from the ceiling of a motor car through a light string. A transverse pulse travels at a speed of 60 cm s⁻¹ on the string when the car is at rest and 62 cm s⁻¹ when the car accelerates on a horizontal road. Find the acceleration of the car. Take g = 10 m s⁻².

Tension = T = mgSpeed = v1 = √(mg/ρ)At motion:Tension = T = m√(a2+g2) and Speed = v2 = √[(m√(a2 + g2))/ρ]Now,or (A - 1)g2 = a2a2 = 0.140 x 100or... View Article

A 4.0 kg block is suspended from the ceiling of an elevator through a string having a linear mass density of 19.2 × 10⁻³ kg m⁻¹.

Question: A 4.0 kg block is suspended from the ceiling of an elevator through a string having a linear mass density of 19.2 × 10−3 kg m−1. Find... View Article

In the arrangement shown in figure (below), the string has a mass of 4.5 g. How much time will it take for a transverse disturbance produced at the floor to reach the pulley? Take g = 10 m s⁻².

Solution:Mass density = ρ = (0.0045/2.25) kg/mforce on the string = T = 20 NNow, speed of the wave = v = √(T/ρ) = 100 m/sTherefore, time taken =... View Article

Two blocks each having a mass of 3.2 kg are connected by a wire CD and the system is suspended from the ceiling by another wire AB

Question: Two blocks each having a mass of 3.2 kg are connected by a wire CD and the system is suspended from the ceiling by another wire AB... View Article

A string of length 40 cm and weighing 10 g is attached to a spring at one end and to a fixed wall at the other end. The spring has a spring constant of 160 N m⁻¹ and is stretched by 1.0 cm. If a wave pulse is produced on the string near the wall, how much time will it take to reach the spring?

Here l = 40 cm , spring constant = k = 160 N/m and mass = 10 gMass per unit length = m = 10/40 = (1/4) g/cmNow, deflection = x = 1 cm = 0.01... View Article

A travelling wave is produced on a long horizontal string by vibrating and end up and down sinusoidally. The amplitude of vibration is 1.0 cm

Question: A travelling wave is produced on a long horizontal string by vibrating and end up and down sinusoidally. The amplitude of vibration is... View Article

A transverse wave described by

y = (0.02 m) sin(1.0 m−1) x + (30 s−1)t]propagates on a stretched string having a linear mass density of 1.2 × 10−4 kg m-1. Find the tension in... View Article

Two wires of different densities but same area of cross section is soldered together at one end and are stretched to a tension T.

Question: Two wires of different densities but same area of cross section is soldered together at one end and are stretched to a tension T. The... View Article

A string of linear mass density 0.5 g cm⁻¹ and a total length 30 cm is tied to a fixed wall at one end and to a frictionless ring at the other end

Question: A string of linear mass density 0.5 g cm−1 and a total length 30 cm is tied to a fixed wall at one end and to a frictionless ring at... View Article

A string of length 20 cm and linear mass density 0.40 g cm⁻¹ is fixed at both ends and is kept under a tension of 16 N. A wave pulse is produced at t = 0 near an end as shown in figure (below), which travels towards the other end.

(a) When will the string have the shape shown in the figure again? (b) Sketch the shape of the string at a time half of that found in part... View Article

A steel wire of length 64 cm weights 5 g. If it is stretched by a force of 8 N, what would be the speed of a transverse wave passing on it?

Mass = 5g, Length = 64cm and Force = 8 N (given)So, density= ρ = (5/64) g/cmNow, F = ρv2or v2 = 8 x (64 cm/5g)or v = 32 m/s... View Article

A wave travelling on a string at a speed of 10 m s⁻¹ causes each particle of the string to oscillate with a time period of 20 ms.

(a) What is the wavelength of the wave? (b) If the displacement of a particle is 15 mm at a certain instant, what will be the displacement of a... View Article

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