A heavy ball of mass M is suspendeed 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 ms ⁻¹. When the car has acceleration a, the wave-speed increases to 60.5 ms ⁻¹. The value of a, in terms of gravitational acceleration g, is closest to: (a) g/30 (b) g/5 (c) g/10 (d) g/20

Answer: (b). Tension ∝ geff; at rest geff = g, with acceleration geff = √(g² + a²). v ∝ √(T): (√(g²+a²))/(g) = ((60.5)/(60))² ≈ 1.0168 a² = (1.0168² - 1)g² ≈ 0.034 g² ⇒ a ≈ 0.18g So the answer is (b) g/5.

A heavy ball of mass M is suspendeed from the ceiling of a car by a… | JEE Main 2019 (9 Jan, Shift 1)

Q32JEE Main 2019 · 9 JAN · SHIFT 1Difficult

Speed of Waves

A heavy ball of mass M is suspendeed 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 ms ${}^{-1}$ . When the car has acceleration a, the wave-speed increases to 60.5 ms ${}^{-1}$ . The value of a, in terms of gravitational acceleration g, is closest to:

Show answer and solution

Answer: (b)

Tension $\propto g_{eff}$ ; at rest $g_{eff} = g$ , with acceleration $g_{eff} = \sqrt{g^2 + a^2}$ .
$v \propto \sqrt{T}$ : $\dfrac{\sqrt{g^2+a^2}}{g} = \left(\dfrac{60.5}{60}\right)^2 \approx 1.0168$
$a^2 = (1.0168^2 - 1)g^2 \approx 0.034\,g^2 \Rightarrow a \approx 0.18g$
So the answer is (b) $\dfrac{g}{5}$ .

Report a mistake

Speed of Waves question from JEE Main 2019 (9 Jan, Shift 1)

More questions on Speed of Waves