Question

A block of mass $1kg$ is hanging vertically from a string of length $1m$ and mass/length is $0.001Kg/m$. A small pulse is generated at its lower end. The pulse reaches the top end in approximately

• A. $0.2sec$
• B. $0.1sec$
• C. $0.02sec$
• D. $0.01sec$

Answer 1

Answer: (D)

$0.01sec$

Speed of a transverse wave on a string is given by the formula:
$v=\sqrt{\frac{T}{\mu }}$ ............. (1)

where, $T=$ tension in the string

$\mu =$ mass per unit length (linear density)

In this question :
Tension in the string ($T$) $=mg$ ................ (Newtons Laws of motion)
$T=1\times 10=10N$
Mass per unit length ($\mu$) $=0.001kg/m$
Substituting the respective values in the formula (1)
$v=\sqrt{\frac{10}{0.001}}=100m/s$

Hence, the time taken by the generated pulse to reach the other end at a distance of $1m$ from the lower end:
$t=\frac{s}{v}$

Here, $s=1mandv=100m/sect=\frac{1}{100}t=0.01seconds$