Question

The bob of the pendulum shown in the figure is projected with a velocity $v=\sqrt{gl}$. Which of the following statement is correct?

• A. The pendulum completes the circular path and returns back to point $A$
• B. The pendulum oscillates between $B$and $D$, always reaching to the points $B$ and $D$
• C. The pendulum oscillates between $B$ and $D$, but never reaches $B$ or $D$
• D. The pendulum crosses point $B$ and travels in parabolic path onwards.

Answer 1

The correct option is C The pendulum oscillates between $B$ and $D$, but never reaches $B$ or $D$

To complete circular path, projection velocity required at the bottom most point is $\sqrt{5gl}$
$\because$ Applied projection velocity < required velocity
So, the bob never makes a complete circular path.
To oscillate between $B$ and $D$ projection velocity should be $0<v\le \sqrt{2gl}$.
The applied projection velocity ($v=\sqrt{gl}$) is within the required range of projectile to oscillate between $B$ and $D$ .
So, the bob of the pendulum oscillates between $B$ and $D$ but never reaches $B$ or $D$.