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(A) The correct option is $A$.In a simple pendulum,the total mechanical energy is conserved in the absence of friction. The total energy of the pendul

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will lie on the line $A B$

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(A) The correct option is $A$.In a simple pendulum,the total mechanical energy is conserved in the absence of friction. The total energy of the pendulum at its extreme positions is purely potential energy,given by $U = mgh$,where $h$ is the vertical height of the bob from the lowest point of the oscillation.Since the pendulum starts from point $A$ with zero initial velocity,its total energy is $E = mgh_A$. At the other extreme point $D$,the velocity is again zero,so its total energy is $E = mgh_D$.By the law of conservation of energy,$mgh_A = mgh_D$,which implies $h_A = h_D$. Since $A$ and $B$ lie on the same horizontal line,$h_A = h_B$. Therefore,$h_D = h_B$,which means the extreme point $D$ must lie on the same horizontal line $A B$.

$A$ simple pendulum oscillates freely between points $A$ and $B$. We now put a peg (nail) at the point $C$ as shown in the figure. As the pendulum moves from $A$ to the right,the string will bend at $C$ and the pendulum will go to its extreme point $D$. Ignoring friction,the point $D$

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