A uniform rope of mass 0.1 ~kg and length 2.4 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The speed of a transverse wave in a rope at a distance $x$ from the free end is given by $v = \sqrt{gx}$.Since $v = \frac{dx}{dt}$,we have $\frac{

Vedclass · Accepted Answer

$1.0$

Vedclass · Answer

(D) The speed of a transverse wave in a rope at a distance $x$ from the free end is given by $v = \sqrt{gx}$.Since $v = \frac{dx}{dt}$,we have $\frac{dx}{dt} = \sqrt{gx}$.Rearranging the terms,we get $dt = \frac{dx}{\sqrt{gx}}$.Integrating from $x=0$ to $x=l$,the total time $t$ is:$t = \int_{0}^{l} \frac{dx}{\sqrt{gx}} = \frac{1}{\sqrt{g}} [2\sqrt{x}]_{0}^{l} = 2\sqrt{\frac{l}{g}}$.Substituting the given values $l = 2.45 ~m$ and $g = 9.8 ~m/s^2$:$t = 2 \sqrt{\frac{2.45}{9.8}} = 2 \sqrt{\frac{1}{4}} = 2 	imes 0.5 = 1 ~s$.

$A$ uniform rope of mass $0.1 ~kg$ and length $2.45 ~m$ hangs from a rigid support. The time taken by the transverse wave formed in the rope to travel through the full length of the rope is (Assume $g=9.8 ~m/s^2$) (in $~s$)

Similar Questions

Which of the following is associated with the conservation of forests?

Which one of the following is the ratio of the lowering of vapour pressure of $0.1 \ M$ aqueous solutions of $BaCl_2, NaCl$ and $Al_2(SO_4)_3$ respectively?

Which of the following elements is used in thermometry at high temperatures?

The length of the transverse common tangent of the circles $x^2+y^2-2x+4y+4=0$ and $x^2+y^2+4x-2y+1=0$ is

Assertion: One molal aqueous solution of glucose contains $180 \text{ g}$ of glucose in $1 \text{ kg}$ of water.
Reason: $A$ solution containing one mole of solute in $1000 \text{ g}$ of solvent is called a one molal solution.

Vedclass Test Series

Exam Paper Generator

Online Exam Module