Question

When the point of suspension of pendulum is moved, its period of oscillation

• A. Decrease when it moves vertically upwards with an acceleration $a$
• B. Decrease when it moves vertically upwards with an acceleration greater than $2g$
• C. increase when it moves horizontal with acceleration $a$
• D. all of the above

Answer 1

Answer: (A), (B)

Decrease when it moves vertically upwards with an acceleration $a$
Decrease when it moves vertically upwards with an acceleration greater than $2g$

When point of suspension of pendulum is moved upwards, $g_{eff}=g+a.g_{eff}>g$ and as $T\propto 1/\sqrt{g_{eff}}$, hence $T$ decreases, i.e, choice (a) is correct.
When the point of suspension of the pendulum is moved downwards and $a>2g$, then $T$ decreases, i.e., choice (b) is also correct.
In case of horizontal acceleration
$g_{eff}=\sqrt{g^2+a^2}$, i.e., $g_{eff}>g$
i.e., again $T$ decreases.