Question

For the $y-x$ graph of a transverse wave in a string is as shown in figure. Which of the following options is correct ?

• A. kinetic energy of the particle is maximum at point $A$
• B. kinetic energy of the particle is maximum at point $B$
• C. kinetic energy of the particle is minimum at point $B$
• D. kinetic energy of the particle is minimum at point $C$

Answer 1

The correct option is B kinetic energy of the particle is maximum at point $B$

From the given $y-x$ graph , we can deduce that ,
$y_A>y_C>y_B\Rightarrow y_A^2>y_C^2>y_B^2$

Multiplying with $-1$ we get

$(-y_A^2)<(-y_C^2)<(-y_B^2)$

Adding square of amplitude $A^2$ we get

$(A^2-y_A^2)<(A^2-y_C^2)<(A^2-y_B^2)..........\left(1\right)$

We know that , Kinetic energy of a particle executing SHM about $y=0$ is given by

$K=\frac{1}{2}m{\omega }^2(A^2-y^2).......\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$ we get, $K_A<K_C<K_B$
Therefore, kinetic energy is maximum at point $B$.
Thus, option (b) is the correct answer.