Answer

Verified

426.6k+ views

**Hint**To solve this question, we have to determine the speed of the sound in the rubber tube from the formula given as $ v = \sqrt {\dfrac{T}{\mu }} $ . Then using the general formula of the speed in terms of the distance covered, we can find out the value of the time required for the pulse to reach the other end.

**Formula Used**The formula used in solving this question is given by

$\Rightarrow v = \sqrt {\dfrac{T}{\mu }} $, here $ v $ is the speed of the wave in a string having the mass density of $ \mu $, which is stretched by a tension of $ T $ .

**Complete step by step answer**

Let us consider the tension in the cord as $ T $

So the free body diagram for the mass $ 5kg $ will be as,

From the condition of vertical equilibrium we get,

$\Rightarrow T = mg $

According to the question $ m = 5kg $ . So we have

$\Rightarrow T = 5g $ ….(1)

Now, the velocity of sound in a stretched string is given by the formula,

$\Rightarrow v = \sqrt {\dfrac{T}{\mu }} $ …...(2)

We know that $ \mu $ is the mass per unit length. So the mass per unit length for the rubber tube, which is of length $ 12m $ is and mass $ 0.9kg $ is

$\therefore \mu = \dfrac{M}{l} $

$\Rightarrow \mu = \dfrac{{0.9}}{{12}} = 0.075kg/m $ …….(3)

Putting (1) and (3) in (2) we get

$\Rightarrow v = \sqrt {\dfrac{{5g}}{{0.075}}} $

Putting $ g = 9.8m/{s^2} $ we get,

$\Rightarrow v = \sqrt {\dfrac{{49}}{{0.075}}} $

On solving we get the value of the velocity as,

$\Rightarrow v = 25.56m/s $ …...(4)

Now, the rubber tube is struck by the transverse blow at one end. The total distance covered to reach the other end will be equal to the length of the tube. So we have

$\Rightarrow d = 12m $ …..(5)

So, the time required for the wave to reach the other end is given by the formula

$\Rightarrow t = \dfrac{d}{v} $

Putting (4) and (5) in the above formula we get,

$\Rightarrow t = \dfrac{{12}}{{25.56}} $

On solving we get,

$\Rightarrow t = 0.47s $

From the options the nearest matching value is $ 0.48s $ . So we take

$\Rightarrow t \approx 0.48s $

**Hence the correct answer is option (B).**

**Note**

We should not calculate the tension in the rubber tube separately. This is because the tube is not freely hanging but it is fastened to the fixed support below it. So, its weight does not increase the tension in it. Hence, the tension in the tube will be equal to the tension due to the weight of the hanging block.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Which are the Top 10 Largest Countries of the World?

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Write a letter to the principal requesting him to grant class 10 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE