A 4.0 kg block is suspended from the ceiling of an elevator through a string having a linear mass density of $19.2 \times 10 k g m^{- 1}$ . Find the speed (with respect to the string) with which a wave pulse can proceed on the string if the elevator accelerates up at the rate of $2.0 m s^{- 2}$ . Take $g = 10 m s^{- 2} .$

Open in App

Solution

$m = 19.2 \times 10^{- 3} k g / m$

From the freebody diagram,

T - 4g - 4a = 0

$\Rightarrow T = 4 (a + g)$

$= 4 (2 + 10) = 48 N$

Wave speed, $v = \sqrt{(\frac{T}{m})}$

$= (\frac{48}{19.2 \times 10^{3}})$

$= \sqrt{(2.5 \times 10^{- 3})} = 50 m / s$

Suggest Corrections

Similar questions

Q. A 4⋅0 kg block is suspended from the ceiling of an elevator through a string having a linear mass density of

19 \cdot 2 \times 10^{- 3} kg m^{- 1}

. Find the speed (with respect to the string) with which a wave pulse can proceed on the string if the elevator accelerates up at the rate of 2⋅0 m s⁻². Take g = 10 m s⁻².

Q. A 4 kg block is suspended from the ceiling of an elevator through a spring having a linear mass density of

19.2 \times 10^{- 3} k g m^{- 3}

. Find the speed with respect to spring with which a wave pulse can proceed on the spring if the elevator accelerates up at the rate of 2.0 ms

^{- 2}

Take g = 10 ms

^{- 2}

Q. A 6.0 kg object is suspended by a vertical string from the ceiling of an elevator which is accelerating upward at a rate of 2.18 ms

^{- 2}

. The tension in the string is

Q. 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.

A heavy ball is suspended from the ceiling of a motor car through a light string. A transverse pulse travels at a speed of $60 c m s^{- 1}$ when the car accelerates on a horizontal road. Find the acceleration of the car. Take $g = 10 m s^{- 1}$ .

Join BYJU'S Learning Program

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 kg m−1. Find the speed (with respect to the string) with which a wave pulse can proceed on the string if the elevator accelerates up at the rate of 2.0 ms−2. Take g=10 ms−2.

m=19.2×10−3kg/m From the freebody diagram, T - 4g - 4a = 0 ⇒T=4(a+g) =4(2+10)=48 N Wave speed, v=√(Tm) =(4819.2×103) =√(2.5×10−3)=50 m/s

$m = 19.2 \times 10^{- 3} k g / m$

From the freebody diagram,

T - 4g - 4a = 0

$\Rightarrow T = 4 (a + g)$

$= 4 (2 + 10) = 48 N$

Wave speed, $v = \sqrt{(\frac{T}{m})}$

$= (\frac{48}{19.2 \times 10^{3}})$

$= \sqrt{(2.5 \times 10^{- 3})} = 50 m / s$