Exams › JEE Main › Physics

A heavy ball of mass M is suspended from the ceiling of a car by a light string of mass m (m << M). When the car is at rest, the speed of transverse waves in the string is 60 m s⁻¹. When the car has acceleration a, the wave-speed increases to 60.5 m s⁻¹. The value of a, in terms of gravitational acceleration g, is closest to:

1. g/20
2. g/5
3. g/10
4. g/30

Correct answer: g/5

Solution

At rest T=Mg, v=60. Accelerating, T=M*sqrt(g^2+a^2). Since v^2 ~ T, (60.5/60)^2 = sqrt(1+(a/g)^2) -> 1.01674 = sqrt(1+(a/g)^2). Squaring: (a/g)^2 = 0.0338, a/g = 0.184. Closest option is g/5.

Related JEE Main Physics questions

• A sonometer wire of length ℓ has fundamental frequency f0. A bridge is placed at a point Δℓ away from the midpoint of the wire, where Δℓ is much smaller than ℓ. If the two resulting segments are made to vibrate in their fundamental modes, the number of beats produced is—
• Two identical piano wires are stretched with the same tension T. Each wire has a fundamental frequency of 600 Hz. If the tension of one wire is increased slightly, what fractional increase in tension is needed so that the two wires produce 6 beats per second when sounded together?
• Two sound sources, each producing waves of wavelength λ, are held at a fixed separation. An observer travels with speed u along the straight line joining the two sources. The beat frequency heard by the observer per second is
• A body of specific gravity ρ is suspended from a light steel wire. The wire supports transverse standing waves with a fundamental frequency of 300 Hz. The body is then placed in water such that exactly half of its volume is below the surface. What is the new fundamental frequency of the wire, in Hz?
• A transverse wave on a string has displacement y(x,t) = e^(-(ax² + bt² + 2abxt)). This corresponds to a:
• A sound source A emits waves of frequency 1800 Hz and is moving downward toward the ground with terminal speed v. An observer B standing on the ground directly below the source detects the sound at 2150 Hz. The frequency of the waves reflected back from the ground and received by source A is approximately: (Speed of sound = 343 m/s)

⚔️ Practice JEE Main Physics free + battle 1v1 →